It is especially tough when the skill seems to be coming easily to teammates. In the case of my DD, her feelings of shame and embarrassment are equal to the actual fear of the skill itself. She said everyone thinks she is a "baby" - but admitted nobody had actually called her that. I think this is fueling the avoidance behavior. She doesn't want anyone to see her struggle!
That's a small thing to base this on- but I'dhave to wonder about the culture at the gym if that's how she feels.