I haven't used the "BIG Buddy" heater but did have the "BuddY" heater, pretty much the same design. I tried three in fact. The first two I brought back after a couple times use thinking they were defective after they did the shut off thing like you mentioned. The third one I decided maybe it was me or the way I was using it. Wrong, used it about 10 times, it was the heater. Now I know there are some good ones in use because many fisherman love their "Buddy" heaters. Mine were all crap ! Personally I think in their over exuberant quest for saftey and legal protection they have sensors in them that are a bit over-reactive to thier suroundings resulting in a heater (many times) that under heats and over shuts off. AGAIN, not every "BUDDY" heater they sell has problems but way to many do. I think $100 bucks or more is too much money to spend on something that will only, perhaps,work correctly after you spend some more money on filters and or special hoses.
MY solution was the Mr. Heater/Cooker period. No complaints, plenty heat,trouble free, can cook on it, and less than half the price the the "Big Buddy"
Good luck on finding a heater that fits your needs. It's no fun if your freezing!