Doh!
So after re-gluing this thing a couple times now, I've decided that the pad itself is now too worn away and doesn't provide enough of a "foot" for the adhesive to stick to.
I've looked online at several vendors for the pad itself, example:
http://www.automotion.com/interior-mirror-...-1966-1977.html
And I can justify spending $3 for what looks to be basically double-sided tape. But I cannot justify $8 in shipping charges!
Does anyone know of a vendor who will ship this thing in an envelope, the way it logically should? Or am I over-thinking this and I should just go get some actual double-sided tape, then glue it back to the windshield?