Here's how I fixed it and thought I'd pass it on...
Remove the mirror from the car (2 screws) and on the bottom, there is a bolt that extends through a metal piece, through the base of the mirror, and into the frame of the mirror itself. First try tightening that bolt but be gentle as it screws into a nut that held in with plastic. If that doesn't work, remove the bolt and insert a small, cut and folded piece of 400 grit sandpaper between the metal piece and the base unit it rests in. Reassemble and gently tighten it. The friction of the sandpaper will allow it to grip and hold position, unless...
...the nut inside the base has pulled through the plastic and no longer can grab and hold. If that happens, JB Weld the nut back in place with the bolt threaded through it to keep the threads clear. When the JB Weld is partially hardened, remove the bolt and clean any JB weld from it's threads. Let it harden completely and reassemble GENTLY.
It worked for me!
Relax, all right? My old man is a television repairman, he's got this ultimate set of tools. I can fix it.
