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.
Another option is to try melting a bit of wire mesh or even strands of wire wool into the plastic with a soldering iron, or maybe just melt in a few staples across the crack.