At my dd's gym, if there is injury after injury after injury, the first thing the coach seems to recommend is getting the child's vitamin D level checked. Gymnastics is an inside sport and at the higher levels requires many hours - not all of these gymnast get enough sunlight and have lower vitamin D levels and that can lead to cosntant injuries.
Another place to look is food, what is the child eating, is he/she eating properly, if not that too can lead to constant injury.
My dd has been involved in gymnastics for 10+ years and is training level 10, she has had 2 major injuries during this career. She broke her foot 1.5 yrs ago, which was a fluke injury and then just this past June she had her elbow operated on for removal of bone chips. This injury we are not sure what really caused it, over-use, a blow to the elbow at sometime or probably a combination of both. I think overall she isn't doing that bad on the injury scale.