Thanks for the update - it does help!
Could be bad alternator or battery - those are very large electrical loads and could drop the voltage down too low for the system to operate. Should be around 13.8vdc at an idle, around 12.5 with the engine off. Check the voltage with the engine running and no AC, then start turning on things.

Could be a bad ground connection too, but that could be difficult to find.

Autozone or Pep Boys (and others) will check your battery and alternator for free if the voltages are too low.

Any dashboard lights that come on while it's dying?

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FrankenBenz: '87 560SEC with an '02 cammed LS6 and custom 4L60E.
Bling: '87 560SEC, ported/polished, lowered
Lisa: '87 560SEL, lowered