Pallas I sometimes get bored with a song, even songs I've written. But it passes.
Many years ago, when I played sax in a "club date" band, the leader would call the same old tunes, night after night, week after week, I would cringe. Then, one night, I was just about to blow, when I saw a couple in the audience, smiling faces, almost beaming, and it dawned on me - this might be the first time they've heard us play this tune. I felt I owed it to them to play that tune, and every other tune, that night, and every other night after that, the best I could. Because I wasn't just playing for me.
When I am playing for just me, I try to pick songs that have some meaning, or a song that has a lyric, and I think about that lyric, the words, maybe even the composer and what they wanted to say, the message. If you think about the meaning, or the message of the song, you can suddenly play it over and over, and not get bored with it.
John Coltrane liked the song "My Favorite Things" and when his group was recording it, they did 50 takes, playing it into the wee hours of the morning. The take that ended up on the album was 49.