To be sure it's not the microwave itself, unplug it and use an extension cord to route it to another outlet. If it lights up, then it's the circuit to it. If not, it's the microwave. Of course, just using a VOM or AC circuit tester on the outlet would tell you the same thing, provided you have one in your RV Owners Mandatory Required Tools Kit.
It has been reported in the past that wires have come loose from the slot type connections used on the back of the electrical outlets/switches. If no power to the outlet, check that. Breakers don't normally trip for the fun of it, but will if there is an overload. I don't know about your rig, but my microwave is on a separate 20A breaker and not on the GFCI.