OK, so it's got a little grub screw in it to hold it in - that's pretty common on some types of arm... one of my guitars has a similar. You can buy replacement screws from ebay (or the whole arm). If you buy a new one, put a little bit of superglue in the thread before you screw it in - it'll be strong enough to stop it slipping, but not so strong you can't move it if you need to.

Glad you got the bridge back down.... next time you do it, loosen the strings first.. ;)