The small private school she has been attending has been very helpful and very patient, but she still gets upset if she isn't "perfect." Socially she is accepted and popular; academically she is where she belongs. People who know her feel she is "so mature for her age." Physically she is very active -- she's in fifth-year acrobatics, fourth-year tap, third-year ballet, and first-year jazz. Participation in activities has always been her decision. I always encourage and praise her, but I try not to push her, especially since I read about the suicide rate of gifted children. How do I help her deal with this perfectionistic attitude that has her so stressed out at times?
I was really taken with how many scheduled events your daughter participates in. Some of these have been going on for her since the age of two years. While you certainly know her endurance level, it sounds like too many scheduled activities to me. Your bright little girl wants to do everything, but ultimately the decision to participate in extracurricular activities should be yours, not hers. There are many interesting events for her to try down the road (school competitions, team sports, sleep-overs, and just hanging out with friends) and you want her to have time in her schedule and to not be overly tense.
I'm a little surprised that the school peers have not started teasing her a bit about all her crying bouts. This will be inevitable in school if her tears continue. Gently remind her of how this looks to other kids. It would be very helpful to teach her some child-level relaxation techniques she could do even in public. I teach children how to slow their breathing rate and relax their neck and facial muscles (so that the "lump in the throat" goes away). Praise is great, but don't overly praise. (I know this is a verbally tricky one.) Saying "you were the best" gives a child a lot to live up to each and every time.
Finally, the suicide rate is not significantly high among gifted children. Being smart and overly sensitive does not always lead to depression. Having a parent or mentor who thinks you are terrific no matter what, and knowing how to enjoy and accept life, are two great proven safeguards against emotional problems for gifted kids. Good luck.