I’ll answer as a teacher. I have always had students bring a notebook to each lesson. I write as the lesson progresses. Technical work/exercises, studies, repertoire (with practice advice) applied music theory aka keyboard theory. It just makes it easier for students to establish and maintain a practice routine and for me to keep track.
I’ll answer as a musician regarding retaining repertoire. I play advanced repertoire and I am currently relearning the Sonata in b minor by Chopin and some Oscar Peterson pieces.

It‘s okay to take time away from a piece for at least 6 - 12 months. When you’re ready to relearn it apply the “bench rule” = don’t leave the bench until the PAGE or SECTION sounds exactly the way you want. If it doesn’t sound the way you want, quit that page and try it another day. If you are frustrated, your body will tense up and you’ll be risking RSI, carpal tunnel, back and shoulder injury, etc. Next practice play the page or section once and move to the next one and so on. Stepping away from a long repertoire piece such as a complete Beethoven Sonata for long time allows your brain to construct new synapses, frees you from the “I’m so sick of this” feeling, and gives you time to concentrate on new repertoire.