that used to be a fairly common problem after they got used a lot. For some reason I don't remember what we all used to do. I think I even fixed one of mine many years ago, but it's pretty vague.
Is it possible that we just "crimped" the area where the outside rod enters the visor? Not sure, but that might be something to look into.
Regarding the inner rod that goes into the wiper motor cover, does your rod twist in both the visor and the cover? Or just one or the other? And what condition is your wiper cover hole in? Even more common than falling visors used to be broken plastic centers in the cover. Leaving the visor kind of hanging there looking for something to hold on to.
Good luck.
paul