The battery protection level is an old feature, your model has a two stage battery protection so there isnt a way to set the voltage level and which point the fridge turns off.
It sounds like your not using leisure batteries as this would result in a rapid voltage drop and hence why you are seeing the red light flashing after 10 minutes.
Cut-off voltage is 10.4, to initially start it requires 11.7V, so even at 11.9 it should be running.
The voltage will drop when its under load, might be worth trying both batteries in series and running it on 24V, and seeing what happens then. It sounds like the batteries are just not heavy duty enough for the current its pulling (15A).