,I have ideas you might like. Obviously the frame and panels are durable,otherwise they would have broke instead of just coming apart during windstorm. I believe panels came out because they flexed. You don't need to build another structure,you only need to find a way to prevent panels flexing. Doing that doesn't require a highly skilled carpenter,the average diy homeowner or handman can easily do a good job. What I perpose is adding "stiffbacks" across panels prone to fall out during wind. "Stiffback" is simply strips of wood,plastic or aluminum spanning panel and fastened in place with screws. For example one could rip 3/4"x3/4" strips of wood on table saw then fasten them to panels with WASHER HEAD SCREWS or plain screws with a washer to prevent head pulling through panel when stressed. Really heavy duty aluminum window screen frame would work as well as countless other narrow strips. I'm thinking maybe corner to corner X pattern might reinforce best but your guy may have ideas of their own. It might be possible to flex panels enough to force back in without disassembling frame. To be on the safe side to prevent cracking panel I'd pre-drill holes rather than allowing screw to make it's own hole,or use seld drilling screws with aluminum. Once panels are in place make sure to ancror and brace frame to prevent movement and twisting.