We'll see how long this fix will last. The top hinge pin disappeared as its surrounding plastic broke away. I drilled a hole through the top of the door and dropped a roofing nail (large head) through the hole and the hinge and carried on.
Nice fix.
I have the same problem with mine. I used a bungee cord the last few times to hold the door closed. I was thinking about installing a set of regular door hinges from Home Depot, like I've seen a few others on here do, but the nail trick seems quick and easy.