At the very bottom of a glass frame arm there is the little bracket with a loop on it - which I guess keeps the arm more stable once it's installed in the door. I'm thinking the frame arm and the bracket are both made out of pot metal? How can I re-attach the loop bracket back onto the arm?

To update, I'm talking about the vent glass frame on a 1970 b body.

If you mean at the very bottom, thats not pot metal but galvanized. I had a friend handy with a welder tack them back on. Worked great.

I Mig / Tack welded mine back on, it was broken off.

I Mig welded mine back on too.
Drill a hole in the bracket where each spot weld was. Then grind away some of the galvanizing surrounding the hole so you (or the guy welding it) aren't breathing the fumes when welding. Just plug weld with your mig and you're done.

This is very common on B bodies, I fixed two of my cars as described above.