I know this is an old post, but did you find a solution?
2 or 3 years ago, I had, what sounds like, the same problem. Dometic was not aware of the problem and were not to interested in helping since I called just after my warranty ended.
I checked the fuse in the 12V cord and it seemed ok.
My cooler with optional freezer compartment has an "Emergency' switch on the front, and when I slide it to 'on', the cooler worked (but constantly running the compressor). Also plugging into my inverter with the 120v cord also caused it to run normally.
Dometic sent me a new 12V cord - I was skeptical that that would solve the problem because our 12V cord was never abused - but that new cord worked!
We've had another 2-3 years of no problems with the 12V powering the cooler.
But just this week, the old problem is back. 12V does not work, but 120V does.
I assume it is the cord, but cannot figure out why. I replaced the fuse just to be sure. No better result.
Dometic has no solution. They say try another outlet, change fuse, make sure battery is greater than 12.8V. Same result using 12V ports in other vehicles. New fuse does not help. My battery is greater than 13V...
If anyone has a solution, it would be appreciated.
Thanks