Since the fridge works correctly on AC, there must be something partially blocking the gas flow to the burner. Check the area around the burner orifice to see if dust or other material has built up there. For a downloadable manual, go the www.thetford.com, and select your model number from the list. On the right side of the screen, choose the manuals tab, and select the manuals you want.
If my answer helps you, please click on the 'accept' button. That's how we experts are paid for our efforts.
I tried to blow out the area through the inspection opening. That still didn't help it. tonight I am going to take out the orifice and see if it looks like it may be partially plugged. If there is nothing wrong there, what is next step for me to try. Also for your info the manual says the gas part will not work as well as it should above elevation 5500 feet. I live at 8300 feet. But up until now it has functioned perfect at that elevation. Last weekend we had it down at around 5000 feet or lower and it didn't cool at that elev.