What's best way to keep shower faucet handle from dropping?
Saw this thread as I was having the same problem.The square socket is not stretched, it doesn't hold the handle in the wall (I thought the same thing at first). Here's the fix: pull off the large chrome/silver plate with the word KOLHER on it, it should pull off as it is not screwed into anything. It might have been caulked on the wall around the inside rim by the previous owner/installer to prevent water from getting in, but should pull off- just be careful not to pull out tiles. As someone else pointed out, the handle assembly actually should screw onto the black threaded part in the wall- it's just tricky and weird. It may be that the parts attached to the wall are too flush/recessed to the wall and the threads in the handle can't get onto the black plastic threaded part.

Now, with the chrome KOHLER plate removed from the wall, you will see two gold/brass screws, one on top and the other on the bottom. These screws hold the larger silver wall plate on the wall (the plate covers the hole in the wall). Loosen the gold/brass screws a bit, this will allow the plate against the wall be less recessed, and the black threaded part will also move out of the wall a bit. Put the metal KOHLER plate back on, and try to attach the handled by screwing it onto the black plastic part. The handle presses onto the KOHLER silver/chrome plate and holds in on the wall.

If it won't attach onto the black plastic, unscrew the gold/brass screws a bit more again to allow the black plastic part to be closer to the handle so that you can screw it on. I had to loosen the brass screws a few time because as I would get the handle on the black part and it screwed on, when I would tighten it firmly, the handle would pop off the threads because the black part was still too short.  When pressing the handle onto the KOHLER silver/chrome plate, the KOHLER plate may spin. I actually got the handle screwed on a bit and started to just spin the KOHLER plate, which spun the handle and tightened it to the wall very nicely. This way, no glue/adhesive is needed.

Once you get it on, and understand how it works, you may want to take it all off and use caulk on the KOHLER ring to prevent water from getting in. This may protect water from getting in behind the wall.