I would suspect you're loosing power on one of the legs (or neutral).
Could be somewhere in the path or the power post, your plug or cable, EMS power protector, transfer switch, or circuit breaker box.
It's a matter of getting a voltmeter out and start checking everything, and making sure all of the wire connections are also tight and secure.
If you have an EMS power protector (like a progressive), then it could be it's detecting low voltage on one of the legs, and then shutting down the power to the coach. When shore power is within correct range again, it turns back on until it detects another error condition. Progressives have displays which will supply an error code, if this is your problem.
DaveB, Raleigh, NC
2015 Tiffin RED 33AA, w/Honda CRV
VMSpc, Magnum BMK/ARC50