The same thing happened to my Passat a few months ago. Luckily mine was still hanging on by a little spot on the corner. It looks as though water slowly edges in and wares away the adhesive. I'd recommend using the black 3M double sided stick foam rubber. Its available almost everywhere in an 1" wide roll. I have some 4" by 6" squares of it that were a byproduct of my dads work. I think sheets of it are available at retail but cant tell you where to find them.
I still haven't put mine back on yet but I think the black part left in the housing may really be the mirror backing. A small part of this was still on the mirror in the corner and revealed a white surface in the housing. It and the back of the small piece on the mirror had sticky stuff on them. You may be able to pull off the black part and stick the mirror directly on the white. Jimi Polivka '91 Passat GL
