Give up on a piece?

There are more options than just giving up or not. You could put it away for some months while continuing to improve as a player by practicing other things and see if it comes easier to you then. Or you could make it long-term piece and only practice it occasionally, like once a week, depending on how many pieces you are comfortable working on simultaneously.
I can't help you decide. Personally, I take difficulty ratings with a huge grain of salt. As players we have different strengths and weaknesses so difficulty is not a one-dimensional scale, nor do people universally agree on what is meant by beginner or intermediate.

I think this kind of decision is very individual. I usually put such a piece on a shelf and come back to it after a couple of months or later if the piece requires too much work at the moment. But how much is too much only you can tell.

I don’t know if you do technical exercises, but if you do, you could extract those tricky measures from the piece and add them to the exercise part of your practice session for some time.

Re: how the composers/arrangers define the levels of pieces - I wouldn't rely too much on those, as there is no universal pattern of rating the difficulty, and every one of us learns different things in different time and find different things easy or difficult. I have recently learned in a relatively short time a piece that was graded as "early intermediate", but found another piece labelled as late beginner much too difficult to learn right now

Animisha I am afraid some months would not make much of a difference. If it is too difficult now, it will be too difficult in March.

You might be pleasantly surprised. Sometimes giving a piece a break while practicing something else can have benefits you wouldn't have imagined.

My strategy would be to treat it as a long term project. If the piece inspires you, it's a shame to just give it up. You don't want your whole practice time to be taken up with something you're really struggling with, and you can't know in advance how long it will take you to get to a satisfying level with that piece. If you stop playing it for a while, and then come back to it, and do this a few times, you will start to get a feeling for a possible rate of progress. You may think that in a year's time you could be playing the piece in a way that gratifies you. Or you may finally decide that it's not worth the struggle. In both cases you'll have gained something from the practice on that piece.

Spending time on a piece without sufficient progress makes it difficult to maintain motivation - often getting to the piano at all, not just that piece.

(My opinion is that no passage of only a few bars should be worked on with more than two or three repetitions at a time. These passages need to be sorted out during sleep, not at the keyboard. The time spent is largely wasted as far as progress goes on that piece and could also have been better used on a different piece - a double dose of waste! I aim for two twenty-minute sessions with a few hours between each to cover all my pieces.)

How does the tempo in this piece compare with your usual fastest playing? If it's in the same realm then you have enough ability to play any passage at about that speed (rate of finger fall not metronome tempo).

Is it possible that it's a fingering issue? You say the tempo is applied by the arranger so this may be a fingering issue in disguise. Consider, for example, passages where the LH plays above and below a RH Alberti figure or where the LH takes the lower note of a RH figure that you may not be distributing properly.

With fractures that are only a few bars, drop all but those few bars. Get those bars in your fingers regardless of tempo - anything countable is enough. Only when the playing is fluid need you worry about tempo. The first rapid rise in tempo happens when thinking time goes, the next happens when recall time goes. Tempo beyond that may need longer intervals of time.

Simpler 'fast' pieces will help to bring up your fastest playing speed. I don't know where you are on your journey but consider (in roughly ascending order of difficulty) Bach's Musette from the AMBN, the final Allegro from Haydn's Sonata Hob XVI/8, Benda's Sonatina in A Minor, the Presto from Clementi Sonatina No. 5 or CPE Bach's Solfeggietto as pieces for bringing up your finger speed.

Animisha Mmm, so you've spent around 5 hours on 4 measures, but you are still struggling to get those 4 measures up to a speed that you think would sound reasonable. If there are 43 measures in total, going at this pace might require about 50 hours more work... that might seem like a real grind. Perhaps if you park this on the back burner then revisit the piece in say, 3 months, it might be more manageable for you?
Is it a Chopin piece, by any chance? I have a similar situation with a Chopin piece in my Alfred's book 2 that is too difficult for me, and I've seen comments online where people say that the piece seems too advanced to be in book 2. I've played the first 8 measures then parked it, because although it's beautiful I'd rather wait until I'm ready for it than spoil my enjoyment of the piece. It's frustrating, I feel your pain.

RFox My opinion is that no passage of only a few bars should be worked on with more than two or three repetitions at a time. These passages need to be sorted out during sleep, not at the keyboard. The time spent is largely wasted as far as progress goes on that piece and could also have been better used on a different piece - a double dose of waste!

Agreed. Spending this much time daily on such a short section immediately brought to mind the suggestions from Molly Gebrian's book. At the very least, I think you would benefit from taking some time off from this and working on other stuff.

Another aspect that I haven't seen touched upon in this discussion is the question of what your own deeper reasons for playing the piano are, and if practicing this particular piece right now aligns with those reasons, whatever they are. I'm not expecting an answer, just trying to provide food for thought.

@Animisha you wrote in another post that you are subscribed to ArtistWorks with Zachary Deak. Have you sent these measures and asked for feedback on how to practice them? If you haven’t, I would do that. If you feel you’re still not making much progress after implementing the instructions on how to practice, then I’d reconsider the piece. But it’s possible you just need some guidance on what’s not working and how to practice it so that it does work.

Animisha What is the piece?

It was I, not JB_PT, that proposed the initial sort-themselves-out-during-sleep idea. Let me try and explain...

Animisha wrote

I practise these four measures. I figure them out, then I put my metronome on 50 for each 16th note, I work my way up until I can put the metronome on 70 for each 16th note (no, not with blocked practice but with interleaved practice).
I go to sleep.
Next morning, I have forgotten how to play those four measures. Once again, I figure them out, put my metronome on 50 for each 16th note, and work my way up to 90 for each 16th note.

This is the problem: 1. During the 'figure them out' stage through the slow metronome phase you're using an initial sort out and reinforcing it while trying to coordinate the playing with a metronome. 2. Then you're trying to do the same some time later with a faster metronome. 3. Then you're expecting to remember them the then next day.
It doesn't work like that.

1. Figure out the measure into workable sized chunks that won't tax working memory - we're not trying to memorise the passage overnight, just trying to figure out a solution. Play it at the speed of no mistakes. This may involve holding down all the notes that are played together, relax all the fingers consciously, figure out the next note or note group, figure out (still holding down the current notes) what fingers will play, rehearse them in your head, imagine the voicing and dynamics if you're that prepared, make the change as quickly as practical and hold down all the playing notes. Repeat the process – hold the notes down, relax all fingers, figure out the next notes and fingers, rehearse the change in your head, make the change as quickly as practical, hold the notes down.
   Continue this way to the end the bar or the end of the fracture.

If it's a four bar passage you might need to work each bar individually stopping on the first beat of the next bar not the last note of the current one.

Don't try to remember more than each note/beat change. Don't repeat this more than two or three times at any one time and ideally clear out the working memory with another piece between each repeat. This isn't about memorising, it's about reading afresh, thinking it out afresh and playing afresh each time. This is about fixing a passage you can't play at reading speed. If the brain wants to remember it then let it but don't add tension trying to memorise it.

Then sleep.

Example 1: If this were bar 1 of Chopin's Prelude No. 20, there would be a long pause after each LH chord. The sixteenth notes just before the fourth beat would be rehearsed as moving straight onto the fourth chord while still holding down the third chord. You might work up to the first chord in bar 2.
Example 2: the Rondo from Mozart's Sonata in C, K545, the double blind jump of each hand in bar 10. Hold down the B in RH and the D in LH. Rehearse the jump to E in RH in your head, then the jump to E in LH, then both jumps together (all while still holding down the B and D with relaxed hands and fingers). When you're ready make the double jump and finish the measure plus the first four notes in bar 11. (If you're planning a performance of this you might prepare to repeat the D in RH or quickly change the fingering to play FDCB, G# in case you jump to the D or F in error. I wouldn't expect to get the LH jump wrong or you can look at the low B while you're playing and make it a blind RH jump only - just for performance, mind!)

2. Don't try to speed it up on the same day. If you're adding a second session five or six hours later repeat the first attempt. Trying to speed it up is adding tension into the passage that may take more time than you'd think to eradicate. Tension is the enemy of speed. Slow, steady, easy and relaxed is the way to go. A better idea is to hum the melody in your head and work on better phrasing. Don't try to play it again, even in your head.

3. If you don't remember the passage the next day but you were trying to then you were doing too much so break the passage down further but that's not what this practise technique is about. The memory used is all working memory, and clearing that out is more important than storing anything. A passage you can't play is a source of tension. Don't build that into your piece. Either make it playable first or memorise the piece aurally before you tackle it at the keyboard.

Now, if you do this for a week (five days) your thinking time is likely to have reduced and your tempo increased from, say, 10 seconds per change to one or two. That's progress. You're still making every change with relaxed mind and fingers and you're playing the passage five times faster than when you started!

I would drop the passage for a week at this stage and work on another piece. When I get back to it the brain should have made everything run a little smoother and a little easier. You can repeat as is for another five days or you can double the length of the passage depending on progress, or the number of such passages per piece. Eventually the thinking time will be fast enough that you can play at the speed of slow foot tapping or beat counting. Then, and only then, need you start with the metronome.

Try it for two or three minutes a day with a new piece/fracture and see how it works for you over a number of weeks.

It's OK to put a piece on hold, for whatever reason.

I find it interesting that you can play it at about 50% speed. My thought would be to quit focusing upon it so much but fairly often, come back and play through it at 50% speed knowing what it is, but just come back and do that often. If you keep doing that, you may find that it'll become easier to take it to maybe 60%. And it's OK to leave it there for a while. Etc. It may take a year or two before it "clicks" and becomes something that your fingers remember, not just your brain, and suddenly, it's as though you're not making it happen, it's just flowing out of you.

I have occasionally had tunes that I tried that just did not work that for whatever reason, I revisited some time later and all of the sudden, they clicked. No idea why.

Maybe some players are different and can remember things exactly for long periods of time. I'm someone who forgets. If I don't actually play a tune for several months, it's sometimes a little iffy as to whether I'll remember it right. I seldom play with any kind of music other than maybe a lead sheet but the similarity from one song to another can be close enough that without concerted effort I could very well start out playing one song and end on a completely different song. Doesn't happen when I play through them fairly often. Ones I haven't played in a while, though... dangerous for me, at least in any situation that matters. Interestingly enough, at least to me, I have had instances when I've had to play for a singer and a song I couldn't exactly remember, but as they sung it, it just "came out". I have no idea how that works but have experienced it numerous times.

This music thing is fascinating, and goes way deeper than the intellectual playing of notes in organized sequence.

Have to consider how far you are able to go with the piece. If you managed to learn all the notes but not yet able to play it at a desire tempo, you are close to getting it to a performance level. If you have not yet mastered the notes, you may decide to drop the piece for the time being due to technical reasons.