[rfeenstra]

I haven't had much problem with the wires coming loose. They are usually wrapped around the terminal several times. I would try to solder the wire to the part that is protruding that is within your drawn circle. Any connections to the top of the terminal can then be soldered quickly so the heat does not have time to transfer all the way down to the coil wire. Secure the wire on the surface with some sort of adhesive.

[RodB]

I would tin then solder a short piece of 24 gauge wire to the terminal then connect the winding to the short piece. In effect, extending the terminal.

Rod

[Radioroslyn]

Looks like you have enough wire left the resolder it to the terminal. Would clean off the old solder w/a solder sucker or wick. Wrap the wire around the terminal a turn or two. Then resolder. The wire has cotton or silk covering which most of the time can be carefully removed with a fingernail. The wire under the covering has a lacquer coating which the solder will burn off.
If you don't think you have enough to wrap around then use a strand from some stranded wire. Wrap it around the terminal and solder. Solder the other end the broken wire on the coil.

[jkaterenchuk]

Thanks for the good suggestions. I will try a repair first.

John