This is a great question. Every teacher has a different approach when it comes to progression, and in my opinion, I think there has to be a balance. I’ve had teachers spend months and months on one piece with me in my learning career, which I think can be discouraging and not as efficient for a student’s progress. I’ve also had teachers go through a piece a week, even if the student doesn’t learn the piece very well. I think either of these approaches can cause problems with learning efficiency and ability to become a better player.
My approach is that a student should learn a piece to 85% perfection before moving on. This means that if a student plays a piece and makes a few mistakes, I will mention them–but if it is only a few mistakes throughout the whole piece, I will suggest we move on to another piece. This normally results in an assignment of students working on 2/3 of their music for the upcoming week if they didn’t practice a lot, and 1/3 of their music if they did practice a lot. It is rare that I tell a student to work on the same exact music for the following week, as well as telling them to work on all new music for the following week. Keep in mind what I consider moving on–if I assign 16 measures of a piece (say that is half the piece), moving on would mean continuing to the very end of the piece.
What I find is that by going to 85%, you are not dwelling on anything, but at the same time learning a piece well. In the future, the student will find the piece that was learned at 85% a lot easier, and be able to get it close to 100% just by becoming a better player. To become a better player it takes learning new combination of notes, and dwelling on one thing for a long period of time can make learning not as efficient (and discouraging) in my opinion.
So in summary–find a balance! If your private teacher is leaning on one side or the other, I suggest pointing out to them that you are feeling there isn’t enough balance there. If you say it nicely, it shouldn’t offend the teacher, and just focus on how you would like to learn, and not that they are teaching you incorrectly.