There is a way of helping with the shaking and falling down but it will not stop it. The mirror its self has a little bit of space all the way around in side of the plastic, that causes more moving and falling then if it was tight. Best way to fix this is to fill the space with 3M's VHB tape. On a hot day I used 2 smallest allen wrenches to hold open a gap at the top of the mirror, cut a piece of the tape down to about 1/8" x 3/4" and used a 3rd small allen wrench to get the tape into the gap. Just don't try and pry with the allens they are there just to hold open the gap, use your fingers to open up the gap, the glass in the mirror is thick but you still don't to risk chipping the glass. Using allen wrenches is important because they have flat sides and are less likely to chip your glass.
http://www.aleromod.com/forums/showthread.php?t=30660