Do you hear the motor run after it turns off?

It's probably not the motor since it still opens.  There are 3 parts that
can go wrong if it's anything like the C4 lights and it probably is.  The
nylon gear, the nylon bushings or the piece that holds the bushings.  My
guess is that it's the nylon bushings.  Take it apart and replace them with
pieces of a steel rod the same diameter and cut to the same height.  If it's
the part that holds the bushing, it's usually that the cast piece has
stripped from the steel rod.  I fixed mine by drilling a hole close to the
bottom, through the rod and then inserted a roll pin.  I went through the
thick section.  If it's the gear, I replaced mine with the brass
replacements from Ecklers.  Everything's still running fine and it's
stronger than ever before.

Hope this helps.  BTW: Replacement motors from the dealer for a C4 runs
$400, not including labor and they don't sell individual pieces to fix them.

There is a TSB for this.  It just needs some washers to adjust it.
You can read the TSB here:
http://corvetteactioncenter.com/kb/question.php?qstId=252

If you need more help, try www.corvettemechanic.com or www.c5forum.com