I've had a couple of this style of plastic clip crack. Wrapping it in thread and then applying super glue seems to work pretty well. I also tried wrapping with fishing line, but it came undone pretty quickly. Just wanted to share the tip! Now if only I had a fix for when the prongs on the other half break off.
It's come in handy for so many of these types of things that I've lost track. Occurrences line these aren't a concern anymore, just find out make a model and boom, good as if not better than new.