A/C is run off the high voltage bus, not the 12 volt bus. Weird stuff can happen when the 12 volt is low.
Can you at least use a voltmeter and measure the voltage of the 12 volt when the car's off after it has sat overnight or many hours? If you are on your original 12 volt, I wouldn't be surprised if it's toast by now. Mine bit the dust in ~2.5 years from date of car's manufacture. Was replaced for free under warranty.
'13 Leaf SV w/premium package (owned)
'13 Leaf SV w/QC + LED & premium packages (lease over, car returned)
Please don't PM me with Leaf questions. Just post in the topic that seems most appropriate.