Very common.. Check the outlet it's plugged into.
here is the thing.. Many RV's (Most i suspect) they use outlets of the "Quick Box" type, this is an all in one outlet, box and cover.. you can tell them from standard house outlets because the screws in the cover are in the corner (on a house outlet the screw is in the center).
On these outlets there is a piece of metal, or 3, inside with slits cut in them, the wire is pressed down into the slot and the metal cuts thrhough the insulation and makes a knife edge contact with the waire, Very little contact area, fairly high resistance when compared to a proper wire under screw type connection.. These "punch down" connections are great for telephone use (Few thousands of an amp) ok in the single digit range, but SPACE HEATERS draw 12 amps (most of them.. I had one that drew more and have two that draw less) this is just too much for the wiring and burns out the connection..
What makes it worse... Many RV's the outlets are daisy chained, So not only the outlet you plugged into but others are affected,, Sometimes the burn out is "Up-line" from the one you plugged into.
How to avoid
If you DO NOT have a washer/dryer bur are wired for it this is a stronger outlet (often a 15/20 type).
On my coach the locaton of the power distribution center (Breaker box) is such that I was able to EASILY add two outlets without tearing walls apart.. one in the bedroom one in the living room, they are 15/20 amp types, fed with 12ga wire bent around a properly tightened screw and each fed by its very own circuit breaker, Nothing else on the line... Work great.
Home is where I park it!