One of the least invasive ways I've seen some accordion makers fix a falling stop is with a small amount of melted reed wax placed above the stop block on the inside corner of the faceplate.
With the treble side removed from the bellows and while the loose stop is in the down position place the melted wax in the corner where the faceplate meets the top block of wood so that when the stop is pulled back up into the open position it sticks to the hardening wax and creates a lot of resistance which in turn prevents the loose stop from falling back down. Just use a very small amount of wax so you don't cause a mess.
I usually use wax around the rod where it screws into the stop block, thinking that if the rod is loose in the frame hole, it's probably leaking air. I also have smeared a little on the slide itself, and glued a thin ship behind the slide to give some friction.
Absolutely no lacquers, f.i. nailpolish stuff has prety nasty solvents ... wax the axle a little, or use something removable like rubber band, a plastic collar made from an old ballpoint pen or clothes pin below the stop to keep it up ... Nout