I had the exact same problem on my '97. Started off with the driver's side moving a little bit, then eventually a lot, then the passenger started moving a little bit. It actually got to a point where I would be driving down the highway, and the drivers mirror would be resting against the window. Anyways, I wasn't able to find a way to "repair" this problem, so I just searched the internet for a few months until I found replacement mirrors. of course, I didn't replace them with the same power chrome mirrors. I upgraded them to a used pair of black plastic power mirrors from the '98-'01 model Rams. the mounting hardware is all 100% the same. Only difference is the wiring harness' are different. Here's the post that I made here months ago when I swapped out the mirrors.
Hope this helps ya out some. Good luck.