I'm a little unclear as to what's happening here...

Are these CA type hinges, or the two-piece-with-a-pin-holding-them-together type?

If they are CA, you could try adding a few drops of thin CA and see how it holds up (Check them periodically)

If they are the nylon type, don't use CA on them, you'll only get glue in the hinge point.

Something else you could do is to push a straight pin through from the bottom. Insert the pin until it JUST breaks through the hinge, then cut it off with a cutting pliers. This will leave a nub sticking out. Now push the nub under the surface and you're done.