We have the same rig as you do. Check in the cabinet under the TV and you should find one duplex outlet and one single outlet. Ensure your fireplace is plugged into the single outlet as it is the only outlet on the 15 amp circuit breaker labeled "fireplace".
Now for the GFCI. We full time and we have had to replace the GFCI in the bathroom twice already. They do go bad, especially when you use a big amp draw appliance on them repeatedly. And we do...called a space heater. Let us know what you find.
2011 Georgetown 378TS in FireMist
2013 Jeep Wrangler Toad
Kirby the Old Dog, passed but still in our hearts
Max E. Dog, the new pup
Eureka the Old Cat, still hangin' on