if the teacher is really good at what they do, that is, a teacher "who has been fantastic in terms of picking up a lot of bad habits and getting me to work at technique and giving me a good solid rep to learn.
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, you must have patience! when a teacher is really, REALLY good, they should not be begging for you to come to the lesson, but you should feel really happy that the teacher has time in their schedule to fit you in.
Of course, if you feel that the teacher has been slipping a little bit, compared to how they were before, I cant see any harm in talking to the teacher about it. However, be diplomatic - say something like "I notice that you are very busy nowadays with more students than you can handle. If it would be easier for your teaching schedule, maybe you have a good friend who teaches piano and has more time for lil ol' me."
if the teacher says yes, then you say "I still would really like to see you! Perhaps we could split my lessons between you two teachers, so neither of you are swamped with too many students"
the key - make their mistakes seem like your fault. They cant get angry at you for that because they will realize whos fault it really is.
talk talk talk. It's the only way to have a good relationship with your teacher