You know, DD6 started violin at four only because sister got to take piano and she wanted to take lessons. She wanted flute or violin, I thought violin was a little more reasonable. I'm glad now, I took a chance, I thought she was too young to start at the time.
I am glad to start the thread as I liked Kriston's comment as it made me think about when she is proud of something. Not something I have focused on as a goal. And I think that is something that will be the ultimate motivator.
DD6 started violin like a tornado, she was so hyped up about it. We rented a used violin and said what the heck. Later on, when it got hard and repetitive, she wasn't liking it so much. She did ask to quit several times. I knew that she wanted to quit because it was hard, not because she didn't like it. Also, she had perfectionistic tendencies and if she couldn't do it perfectly, she didn't want to do it at all. That's probably the real reason I didn't let her quit, and I did feel like a really mean mommy some days.
Flash forward to last week. Violin teacher tells us she's ready to go up a size in violin. We tell her that she gets to trade in her ratty old rental for a NEW violin! And even better, it's not a loan, we are buying her a new violin and she gets to pick it out herself. She beamed. We told her she earned it because she never really gave up even when it got hard. She stuck it out and now she can actually play. We made it a point not to tell her she earned it because she was actually good at playing.

She has a lot of pride now, in herself, and treats her violin as if it were very rare and delicate(even thought it's new, it's still a cheap student version!)