Really hard to tell from those photos, but is this bit threaded?
If so, you've lost the nut that goes on the outside. Any guitar shop should be able to find you one.
After comments: I've never had a socket come loose twice. Tighten it properly, it'll never happen again. Bit of superglue on the thread might help too, if you struggle to reach in properly - needle nose pliers don't like being twisted that way ;)
… or get the guitar shop to do it, if they've got a socket spanner that will fit. It's not a difficult job, by any means, just a bit of a tight space to work in.