My daughter is six years old and has just started piano lessons. So far she is thrilled with the lessons and the new piano that we are leasing. My question is this: If she starts to lose interest, say six months from now, what could I say to her to "re-motivate" her with the piano. Also, if this does happen, when do you say "OK, you don't have to take lessons anymore"? I want her to be happy with this experience. I also don't want to be a pushy mom.
Try not to over-analyze this situation. Your daughter is "thrilled" with her introduction to the piano. Rejoice in her present delight and discard any possible negative thoughts you have about her losing interest in the piano in the future. No doubt, you are being influenced by stories of other kids (or perhaps your younger self) who have tired of music lessons and given up their instrument.
I believe that the best parents can do, regarding music or any other child-generated interest, is to provide their kids with a non-pressured introduction to the activity, in addition to their support and encouragement. Monitor whether your daughter and her teacher are a good match and make sure that the teacher is more interested in stimulating your daughter's musical curiosities and love of music than being a strict, demanding taskmaster.