If it is just one of the plastic screw posts(with metal threaded insert) you could attach/sturdy it up a bit with some strong glue. Probably might be a good idea to coat on the sides of and around the other posts with some glue as well.

Either way, you really want to stop moving the hinges and fix this as soon as possible because more damage will result in leaving it.

If all else fails and you _really_ have no other option then you can put a bolt+washers through the whole thing. It is not the best choice though because you damage the exterior plastics.