The shower faucet handles have been getting looser, but once a decade seems reasonable. This time around, however, the setscrews had dug themselves so far into the splined plastic fittings that they had run out of thread:
Wipe out the crud, clean out what’s left with alcohol to encourage stick-to-it-ivity, and fill the cavities with JB Kwikweld epoxy:
When it cures, file a flat across the sockets:
Reinstall in reverse order with a dot of NeverSeez on the setscrews for good measure.
Just so you don’t have to look it up, this is what the cold water faucet innards looked like a decade ago:
Ought to be good for another decade, right?
The Smell of Molten Projects in the Morning 
I think I may have immediate use of this information.
Snug that screw inside the handle!
I hesitate to tempt Murphy, but the Eljer shower handle in the bathroom is still going strong since Dec 1999. I hope it stays that way, because whatever the installers used for sealing the escutcheon plate seems to be stronger than the fiberglass shower surround. Any access from the back will require sheetrock surgery. Nope.
That promises to be an expensive repair if/when a seal goes south.
When I replaced the shower faucets, I thought I did a really good job of smoothing the joint compound over the patch.
Now I can’t imagine how I missed all those imperfections. Fortunately, the patch mostly hides behind the bathroom door, so I must look to see it; avert my eyes and it’s all good.
The only good news is that any holes will be done in the back bedroom (office/hamshack/storage) closet. Being a manufactured home, what the studs will look like will be more interesting than fun. (Fingerjointed 2 x 3s for non-loadbearing walls seem to be the norm. I’ll contain my enthusiasm for later.)
Julie was talking about a new shower enclosure if that comes to pass. I can’t really disagree. Protip: fiberglass enclosures and heavy wooden brushes ensure you will learn about plastic epoxy repair. [wince]