When last talking to a technician about my CFX55 he said that it draws about 15A on startup. I haven't tested whether that is the case but what could possible be happening is your battery may be dropping in voltage as the motor starts each cycle and it may not be starting. Or even running for a while and then cutting out. What colour are the lights on the fridge?
If you have a multi meter a good way to test your battery is to run something like a compressor and measure the battery terminal voltage and watch how it drops.
To test the fridge, you will have a cigarette plug lead so plug it in in a vehicle cigarette socket for a while and you should see the temperature drop after a while. If it doesn't you probably have a warranty issue.
