Dometic Refrig keeps cutting out.

you never said as to whether you are gettin gas or not...

Do you have a thermocouple? Most Dometic models do have one, but quite a few use an ignitor on the board- these are pretty reliable though.
A model number would help.

I cleaned up the ignitor with sand paper and the burner was very clean. It still cycles three times and shuts off. Is there a way to check the circuit board?

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

If you just filled up the tanks or had filled you may have an air lock and the gas isn't theren enough. Start the stove and maybe the furnace to purge the gas

ditto take it off and clean it and clean around the burner tube while ur at it

Your igniter/flame sensor is probably dirty.

dbontherun wrote:
When my Dometic refrig is on LP gas it cycles three times and then shuts off. What might be the problem?

Not sure completely about what happens, but it sounds like what you are saying is that it TRIES to start 3 times then shuts off. That means after 3 tries it did not detect a flame, and then the default is to shut off until power is cycled. If so, it's likely either
a) you don't have gas
b) you don't have a spark
c) something is wrong with the control board
d) something is wrong with the flame detection and it doesn't detect a flame is present.