Something like that might be possible. One challenge is that the
broken piece seems to have a pretty thin plus-shaped (+) cross
section. If you could accurately drill lengthwise into the center of
the "+" with a 7/64" drill, a #6-32 screw would probably cut its own
threads into it. A clearance hole (9/64") in the U piece would allow
you to send in a long 6-32 screw starting from the inside of the U.
I've successfully done some plastic welding, but I find it very
tricky, and IME the repair is never as strong as the original. If you
go that route, I'd suggest melting in as much reinforcing plastic as
you possibly can, far beyond just recreating the original cross
section. Maybe the screw plus the weld would work?
There are lots of plastics that adhesives won't bond. Anything
polyethylene-based is very difficult.
I'd also attack the problem by prevention. First, would it help if
you swung the mirror inward when you park the bike?
Second, what can you do to prevent your bike from falling over? FWIW,
I don't use kickstands, for that reason. Instead I find something to
lean the bike against, and I lock the front brake.
- Frank Krygowski