Uh yeah, they do that. There's a little motor inside that drives
a gear which drives another little gear. The weakest point in this
chain is a fairly small bit of white nylon. Something in this drivetrain
has screwed up.

Hinesly the best way to fix this is to get another mirror from a scrapyard;
the interpart listing at car-part.com shows they range from $180 to $17.
$25 is what I think is normal and reasonable. Having tried to fix mine with
the same problem that's what I'd do.

If you want to try to fix it, push the whole unit back as far as it
will go and use a flashlight to see inside. You'll see the two ends
of the circular springwire that holds the lens on. Unclip them and
you can now pull the actuall mirror off (carefull, or you'll break the
glass. Now go buy a good used one.

You might find a broken plastic bit. What you won't find is a source for
one as far as I know they're not available. Did I mention you should just
probably buy another one? A crime I know, but what ya gonna do?