How to keep worn car visors from falling down ...

Most of the time the best way is replace with used ones from salvage yard.  Very easy to replace.  The problem is getting to the part in the visor that binds on the holder.  Some visors use plastic parts and some use metal rod.  In either case, insert something into place to help bind at the point of friction.  If it's a visible plastic rotator, take a bread wrapper wire tie, strip the paper or plastic off so you're left with only the thin wire and wrap it around the swivle point.  It should slip into the slit and strat binding.  Then just twist it or nip off the excess wire.