It's interesting that so many gymnasts and coaches seem to think that wearing wrist supports weakens the wrists. I suppose it's also possible that wearing a helmet to prevent head injury weakens the skull.
It's been clear for years that wrist injury is not only common in gymnastics, it's essentially the norm: Studies suggest that half to three-fourths of advanced gymnasts suffer (usually chronic) wrist pain, and about half of young, beginning to mid-level gymnasts also suffer from wrist pain. The authors report: "Gymnasts report symptoms of wrist pain as chronic, and perhaps because wrist pain is so common in the sport, it is not frequently brought to the attention of physicians." [Am J Sports Med. 2006 May;34(5):840] Since your child has already suffered a wrist injury well before the age at which such injuries typically occur in female gymnasts (in the years surrounding peak height velocity), you may wish to discuss with a sports medicine specialist who works with child athletes the wisdom of having her continue using the wrist supports while also continuing to strengthen her wrists through gymnastics and conditioning. My daughter's been using Golden Hands (which are similar to Tiger Paws) since she started doing Yurchenko-style vaults a couple of years ago; they help.