air Conditioners

The rear is usually primary with the generator if it's running. On plugged in shore power both can run but one might cut out so other appliances can run. This is done by a system controller that has priority assigned to your demands other than A/C like cooking. It stops the power draw that the A/C demands to insure it does not burn out due to low power levels coming in from any power source. Many shore power,( power you plug into), have various Amperage available due to design and or demand to customers closer to the power entrance from the providing Utility Companies supply lines. The farther away from the source the less power available as it is consumed by the first in line customers. So yes they shut off occasionally, as required, to save destroying your A/C by low power heat up. The longer your extension cord is and the older and any oxidized terminals of the plugs and your circuit breakers are, the less power you get even if full power is present at plug in point.