So-I'm guessing you're at a location that's providing a 30-Amp hookup. Sometimes, with "dirty" power, when you're sucking major power involving two big things: A/C & Microwave, A/C & water heater, Microwave & water heater, etc. You get the idea. . .
What COULD be happening is that at first the A/C fan starts, then the compressor. Compressor shuts off when desired temp is reached. Fan blows a while longer (unless you've got the fan set to always run) then shuts off. The next time it kicks back on, it may not have enough power to start the A/C's motor. So it can lock up and/or shut down the capacitor.
I had a similar problem, there's a modification available (especially helpful if you run your camper on a generator). Replace the stock capacitor with a Hard Start Capacitor. I've tried A/C with a 20-Amp connection, from my solar power (batteries)-the hard start capacitor has solved my situation.
What could be happening is that by disconnecting from shore power and reconnecting you are letting pressures within the A/C system equalize and then compressor motor starts when you try again.
Check out this link - talks about generator and altitude, but could be applied to dirty power, or if you're hooked to a 30-Amp source but getting less?
RV Air Conditioner Hard Start Capacitor | ModMyRV