I too agree it may be the fan.. I have a 750 Watt electric fire place (Fan Blown) which is doing the job just now.. plus a few 1500 Watt space heaters I can back it up with.
NOTE: RV wiring is not really that good at 1500 watts.. I've lost two connections (one outlet, one other) and others have as well running 1500 watt heaters.. Thus I added a couple of dedicated circuits.. NOT via the inverter, and 12ga wire from a breaker (only thing on the breaker) to a 15/20 amp outlet (Wire bent around a screw and "T" shaped neutral) No problems with these circuits.