A bit difficult to answer, because it depends on what you mean with "polish". If having to polish the piece means that you are not allowed to play it very messily, with many mistakes, rushing and so on, then yes, you need to polish your pieces more if you ever hope to reach the standard needed for the pieces you have as a goal. But if you have to spend many lessons polishing each piece, then they likely are too hard and your teacher should give you easier pieces that you can complete faster.Overall - based on my own experience as someone who has gone to music college - I think it's better to play a large quantity of pieces that are at such a level that you can play them well without too much trouble, as well as a few pieces that challenge you here and there, but not too much. Quantity and experience helps building up skill more quickly than wrestling with the same, too difficult piece for months. However, at a certain point a new piece each lesson sounds a bit too quick.If your teacher is a master student she is probably young? Keep in mind that studying for a master in performance does not mean that you know how to teach. Teaching is a whole separate art. It makes sense that she insists on polishing your pieces to a high level, because that's what she'll be doing in her own study, but if it's starting to kill your enjoyment of playing, I think it sounds like it's too much. She might simply not be an experienced enough teacher to see that it's not the right time in your course of study, or in alignment with your goals, to focus on polishing things for months on end.I suggest you bring this up with her and see what she says.
..I'm taking lessons from a piano teacher once every two weeks... I've been practicing for more than two months. We've had five lessons....and we're now working on three pieces:1.Beethoven - Pathetique Sonata 2nd Movement 2.Chopin - Nocturnes, Op. 9, No. 23.Debussy - Arabesque No. 1 in E major.... I feel it’s quite boring to keep playing the same pieces for months .... I think they sound good enough.... However, according to my teacher's standard is still not enough.
I beleive it is a not the most effective lesson setup to merely study a few pieces like this for months on end. What about improving your practice method? Is your teacher certain you understand fingering logic at the piano and are able to solve it in all sorts of situation? Your sight reading is so strong you can read everything immediately? There are many more skills at the piano that need to be developed which will help you deal with more advanced repertoire, it certainly is not simply about playing a few pieces with mastery, that will give a very fragmented perspective if it is the only approach. You should be doing a large bunch of smaller pieces as well and target some piano skills which will help you learn faster. Ask the teacher to give you this along side the larger works you have been doing.