Dometic Refrig keeps cutting out.

As others have said, the burner components might just need cleaning. I had the same problem yesterday, however, after I had cleaned mine. In this case, the thermocouple (arrow in photo) had slipped back just a little. The frig would light the flame; it would burn for a minute or so and then turn off. When I slid the thermocouple into the right spot, all was well. I'd do as suggested and take out the burner and clean it, along with the electrode and thermocouple. While you're at it you could remove the spiral baffle from the flue and brush out the flue too. Good luck.
jor