An inverter is not only ~80% efficient or so, it had a standby current draw even when the fridges compressor is not running. This no load current consumption likely ranges from 0.25 to 0.7 amps on 400 watt inverters.
So the fact that your system has worked well on an inverter speaks more to the capacity and voltage retention of your large lifeline AGM battery. As powering your fridge by the inverter likely used 40 to 60% more battery power than it would have on direct 12vDC.
I had my friends 50 quart ARB for a few weeks and kept it cold via the provided 12v 16 awg cord and the Ciggy plug.
I had the battery protection settings set on minimal, meaning it would not work when battery voltage fell to 10.5v.
But I found that the compressor was not firing up when the battery voltage had dropped to 12.2v.
Basically the 16 awg cord and ciggy plug combo were dropping so much voltage that the battery protection settings were kicking in way too early.
Danfoss/secop are the designers of the compressor and controller in an ARB.
The wire size thicknesses they recommend for a given distance are much thicker than should be required for passing 60 watts. This is because these controllers are susceptible to voltage drop.
http://files.danfoss.com/TechnicalInfo/Dila/06/bd35-50f_electronic_unit_ac-dc_04-2009_ei100g402.pdf
When the voltage is too low, the fan will come on and run, but the compressor will not. Since the compressor is fairly quiet the user might think the fridge is still working because they hear the fan.
Basically the better the wiring is to the compressor controller, the better and more efficient the fridge will be.
Ciggy plugs and receptacles are horrible connectors, but are needed to be provided with any 12v appliance, but are best avoided entirely.
Buying the 12v power cord in the ARB link posted above is a much better option than using the inverter.
But the cord itself is far far from ideal with 16 AWG wire being much thinner than recommended by Danfoss.
If it were my fridge, I would likely cut the cord right near the connector head at the fridge and wire it with 10AWG to the fuse block( 15 amp fuse)
Going a step further, I would likely bypass the ARB connector on fridge body and run 10AWG right to the compressor controller itself. but I did not open up my friends fridgeto see how difficult this would be.
YOur ARB fridge uses this compressor and nearly exactly this same compressor controller( yours has 120V inputs as well)). The two fatter wires on top are the 12v main inputs.
Getting 10AWG directly to these terminals from the fuse block and ground Buss would be ideal.
Next best would be cutting the ARB cord near the connector where it enters fridge body and splice in 10AWG to fuse block.
Next best would be cutting off the Ciggy plug cord and wiring the 16awg directly to fuse block
Next best would be to just plug and play the ARB DC power cord with ciggy plug.
The 12v receptacle you use should be thickly wired. 12v receptacles provided in vehicles are NOT well wired and will suffer considerable voltage drop.
Combine the 16awg DC cord, ciggy plug and underwired 12v receptacle, and the fridge will only work properly when the battery is 80% or more charged. In such an instance your inverter would work better as voltage drop is not a concern on AC wiring.
But if you were to Bypass thin wiring all together and power it by DC only, you would use much less battery power and not have to listen to the darn inverter fan, nor worry about the fridge shutting down due to low voltage due to insufficient wiring.
12v ciggy plugs and receptacles insult DC electricity with their high resistance and low reliability. That they are widespread and ubiquitous and convenient does not negate this fact.
