That's awful! I checked my fobs and none have that type of ring, but I did have that happen to a Betsey Johnson bag. I wore it for less than an hour and a handle came off because the screw fell out. Fortunately, like you I found the screw and when I fixed it, I put superglue on the threads before screwing it back in (and then did the others as well). It's been a couple of years and it's been holding up OK, so it seems the glue did the trick.
That's good to know! I'm going to get some superglue then and see if I can repair it without messing up with the glue!