MWSHAWJR - After my issue with the propane was solved, we were camping w/o hookups without further issue. That is, until shortly after midnight on the first night on propane. Refrigerator starts beeping, and blue LED starts flashing. Of course, the manual we do have (the European version) was worthless. Turned it off and back on, switched to 12VDC, no change. The beeps repeated every 2 minutes - hard to sleep that way. Ended up turning it off until morning. Turned back on in the AM, still blinks and beeps. Turned on genset to try 120VAC; no difference. Ended up switching back to gas and tolerated the beeps during breakfast. Noticed (as you noted) it still cooled. We were sightseeing that day, and noticed after we were on the road 5 minutes or so, no more beeping. Called Dometic USA later that day, got the same response you did (take it in for service). It's worked fine since.
After the fact, I remembered when we were preparing to leave and loading the fridge, the door was open for a bit, and it did the same thing. I suspect that is the door ajar alarm, except the doors were firmly closed when it went off in the night. Maybe something is faulty in the switch. Whatever it is, it's going to be hard to get someone to diagnose a transient problem like this.