Door handle problem

[agnes the dog]

My interior door handle keeps falling off. I have the lever type that rotates on the splined shaft, held on by an allen head set screw. I have tightened the set screw over and over and it only lasts maybe a month. Then it's back to falling off when I shut the door. It appears that the splines are intact, but maybe not enough to hold the handle on?? Anyone have a fix for this? I'm getting too used to opening it from the outside.

I am also considering a way to turn it into more of a knob than a handle. I'm interested to see if anyone has any brainstorms for this.... Maybe threading the shaft and using a flat style shift knob??? Just thinking out loud...