College Rejection

My 17 year old daughter has always been a very disciplined and motivated student.  She gets straight As, and participates in numerous after-school activities.  She applied to a few ivy-league colleges for the Fall, and so far she has been rejected by four schools.  She was accepted by her safety, which is a very respectable university, but she is not dealing well with all of this rejection.  She has never "failed" at anything before and she suddenly feels depressed and insecure.  How can I help her regain her confidence?