sorry to pull this back up (again), but I moved and had to unpack the computer and the toy to take a look...
super glue.
put a drop in the arm-cup, put it on the arm peg and keep it moving for about a minute (if you stop it will harden and it's destoryed) if you keep it moving the glue with not bond the two pieces but instead form a shell on the two pieces that creates a tighter hold. It also works on weak knees.
it's not a loose joint, it's like the cup is malformed. instead of a nice U shape, the top is open like this \_/ and I'm afraid adding super glue (or anything else) inside will make the problem worse. I can't think of anything that will close the top beside sculpting epoxy, and that won't be stable for a joint