I wonder if you have something else adding to the power draw. Maybe the
refrigerator and/or converter or some other 120V device. Or the water heater, though that shouldn't run all that often. The 30A connection is enough to run any two high-power devices (water heater,
microwave, AC, space heater) at once but adding in a third one will definitely overload and trip. The fact that something that runs in short bursts (microwave) trips it makes me think that's the problem and not low voltage/bad connection.
Bad breaker's not impossible (bad calibration, bad return spring on the solenoid), but it's definitely the less likely explanation.