I have a 10" sub in my trunk as well. I see vibrations in my OEM mirror but it NEVER physically adjusts itself or falls, no matter how loud I have Drake turned up
It sounds like your mirror screw is loose (or if tightening doesn't solve the problem... stripped). I suggest buying a new aftermarket borderless mirror with homelink controls online - there's a few on different sites that I have my eye on.
On another note I'm sure you hear all the other ridiculous rattles this car makes with a sub too - mine makes this awful noise somewhere in the backseat, I think it's the 3rd brake light against the window. The door mirror controls in either door also rattle at the right frequencies.