I have 2 GFCI's. One in the bathroom and one in the living room. Both are fine. The one in the living room controls the side our TV is on and the fireplace is below the TV.
The electric fireplace is nothing more than an electric heater with a revolving light display drum... Shouldn't be too hard to track down the problem. I'm thinking GFCI as well... I have three of those circuits in my trailer just go reset all of them and see what happens...