See my 2000 Astro Power Window post.
That's how the trouble with mine started, only it was in the up
direction instead of down. Now that the temps are way above normal (over
100 degrees here lately), it is now taking about 3 attempts to open the
window fully (auto function) and it typically takes me 45 minutes or so
to close it again.
Folks have pointed me at the motor, but mentioned that it may be a track
or regulator problem. I'll post my findings when I get in there and come
to some conclusion.

My guess is that you have a cracked connector - A brand new motor comes with
a new connector!!   8)

I had similar problems in both my '91 Buick Regal and 2001 Bonneville.
The Regal had multiple issues: windows role up and down without
pressing the button, doors locking and unlocking while driving on the
highway (kinda haunted like) and occasionally the trunk would pop open.
This car I did not keep long enough to find out the problem.  The
Bonneville however had similar problem and it turned out to be the
window control module on the drivers door because I liked driving with
the windows open even if it was raining the water left deposits on the
internal circuitry of the controller.  Was about $80 from the parts
store and R/R was fairly simple.  I say fairly because I had to fish
out the spring clamp from between the doors with a magnet because it
popped off when I removed the old controller.

My mechanic installed a new motor and it's fine.  The old motor was
straining badly -- which I didn't realize until I heard the new motor having
a much easier time moving the window up and down.