that has occured to my jeep by the previous owner.
a couple of things.
make sure the screw that goes through the bottom of the door handle it tight. they have a plastic support below them built into the door panel, mine had crumbled away. i glued in some plastic bushing that i had, it had a hole for the screw, now i can tighten it down proper.
next problem on the back of the door panel, the handle is held in by melting over the plastic, this also breaks, probably if the lower screw is not tight.
i used screws through the back of the door panel into the handle. works fine, only if you can tighten the screw through the bottom of the handle...
make sense?
if you have the means to take the panel apart you will see...