As another mother of a dancing 17 year old. I feel your pain..
I think Dancinfeet has given the right advice.
I can't imagine that your daughter means to give up before her performance, as most dancers have such a strong sense of team work and commitment.
I'm clutching at straws here a bit, but I wonder if you could encourage dd to invite some of her college friends to the performance? It may give her a fresh perspective when her friends all admire her skills and talent?
Is she struggling with her college work at all? A levels (if this is what she's doing) are a lot of hard work and time consuming too, and maybe this is adding to her decision to stop dance. if so, is there any support you could arrange for her?
As others have said, it is a time when many young people do leave dance, as you will already know. Alternatively, they go on to full time dance training (not usually the Royal Ballet though!). What, if any, were her original plans to study full time post 18? was she going to take the DDI route to train to teach ballet or a full time course? Maybe she could explore different routes still connected to ballet, that may re incentivise her...
How long has she thought about giving up the ballet? Encourage her not to make a hasty decision. Maybe she'll change her mind again? If you have to give a terms notice, then perhaps you could encourage her to see the next term out and see whether she still feels the same?
Ultimately, I guess you have no alternative but to accept her decision after you've talked through all the possibilities with her and fully explored her reasons for stopping.