Are they velcro
grips? If so, you can just put an elastic over the velcro strap to hold it in place while you take your turn. It might still loosen some, but not enough to be bothersome. For your next
grips, ask your coach if you might be able to look into buckle grips.
(ETA: If they are in fact buckle grips, just tighten them to the next hole--might be tough to do, but they won't loosen quite so much during the routine, and, they stretch out the more you use them)