My guess would be an overloaded automatic resetting circuit breaker that trips, resets, and then restores power. When it does, both A/C units are in start up mode which causes an excessive amperage drain and voltage drop resulting in the automatic shut off of one of the units.
What can you do? Not sure. It depends on where the automatic circuit breaker is at.
You could try by-passing the breaker by drawing power to your RV from two electrical posts, and devoting one post to each air conditioning unit.
Or, there are electrical devices that will correct for low voltage by increasing the output voltage to a full 120. That device would be installed between the power post and your RV, probably at the point where the power cord is plugged in to your RV.