recylce-
"Once it starts back up it never shuts off." That could be the sign of a $5 relay which has worn out. The relay contact points eventually burn and can arc-weld shut when they get old, leaving the circuit stuck "on" forever.
The expensive fix is a new $5 ($10?) relay. The traditional fix is to get a "relay point file" from a shop that still sells tools for ignition point relays, and gently polish the relay points smooth again. If you can't find one of those fossils, you can use a double-extra-fine nail file (glass or crystal type) or a piece of 600-grit or finer sandpaper doubled over so it sand both sides at once.
When cars "all" had ignition points and replacing them was a part of every tuneup (and they cost something like 10 gallons of gas? 20?) it was routine to polish the points that way, to prevent them from sticking.
If you're lucky--that's all it is, a minor control failure, nothing in the AC
lines themselves.