The compressor draws a big spike in each startup. Thinner cable can't provide it in time and the inbuilt low voltage cut off in the fridge thinks the battery is flat, and switches the compressor off (but the fan still runs). This is why you need bigger cable than the fridge wattage suggests.
I've just rewired my fridge as it wasn't performing as it should and it's made a HUGE difference. It was cutting out after less than 12 hours at night time. I never noticed before as I have solar, so my battery shows pretty much full in the morning and during the day. I woke up at 5am last weekend to hear the fridge constantly going on and off. I know the sound of the low voltage cut off

- My battery should be lasting for ever in good weather with solar. The fridge wasn't getting past 5am! - thing is, the rest of the electrics were fine - i.e. the battery was fine. TV, lights etc, all fine.
I had hefty cable going from the battery to the solar charger, and the same back to the fridge, but there were several places where it was interrupted with runs of 2.5mm2 (27Amp) cable, which I thought was enough. I've doubled up the 2.5mm2 cable and now my fridge is performing much better. I've disconnected the solar and I've had the fridge running for 24 hours so far with no cut outs at all.
Danfoss and Dometic both specify that for every metre of cable run to your fridge, you should have 1mm2 of cable thinkness. So 5 Metres = 5mm2 !