This happened to mine a while back. IIRC the mirror sits on a backing plate with two slots at the top which hook onto two lugs and is secured at the bottom underneath with a screw. The backing plate on mine had broken round one of the slots so I made a small plate with a slot in it from thin aluminium sheet and screwed/glued it to the backing plate. Been OK since.
1 - I used pipe dope, the purple and orange combo for pvc pipe. Applied in layers about 45 mins apart, it creates a 'globby stiffness' with some pliability. Allowed the post to be glued back together but then also take new screw that could be tightened quite a bit.