50 amp, 30 amp, or 20 amp? Sounds like a low voltage problem on shore power. If 50 amp service there may be a problem with one leg of the feed. Could be a loose connection where it plugs in.
If you have a voltmeter measure any 120 volt outlet while you try the AC. See if the voltage drops real low (105 volts or less) when the AC comes on. See if it is low to begin with. Compare the reading while on generator power.
If you don't have a voltmeter, try plugging in something that you can see or listen to when the AC cycles. If the item dims or slows down or groans, it could mean a power drop.
If possible, try a different shore connection.
Just flinging some thoughts out there as you haven't given many details yet.
__________________
Jim
Retired electronic technician (45 years in the field)
2017 Greyhawk 29W (solar & many other mods)
wife (maybe I should have given her top billing)
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