We had the same piece of plastic break on ours when a friend stumbled and grabbed the thing to steady himself.
My solution was to remove the accordion door and then fasten a nylon washer to top of the broken piece of plastic. I shaped the washer's surface to match the remainder of the plastic slide so that the surface that rides in the track is even. A screw holds the washer in place. I glued the hollow rivet so that it is secure and won't wiggle. This repair has lasted many years.
If your door is like ours, this is the manufacturers page for the doors:
http://www.irvineshadeanddoor.com/pr...folding-doors/.
Tim