I ran 10 Ga wire to the back of my 4Runner and never have any cutout issues with my Engel 45
Back over the summer, I copied teotwaki's approach. I made (2) wiring harnesses (1 for my Wrangler and another for the wife's Grand Cherokee) out of 10 Ga Coleman wire. I also sleaved the red/black 10 Ga wires and used shrink tubing to clean it up. I placed an inline fuse on the positive cable right near the battery on both as well. I am currently using Anderson Powerpole connectors, but I really don't like them (plastic and not as tight as I want them to be. I want the fridge wiring to be "secured" as in screwed and tightened). I will be changing all my connectors to mil-spec connectors eventually to match my solar generator I built.
Since I installed these wiring harnesses, I have had zero problems with voltage issues... (hell, I left my fridge running last week for 3 days without starting the Wrangler at all (stock 60ish Amp Hour battery) with the fridge set to 28F full of beer and various stuff) The problem is that the cigarrete (spelling? don't smoke... lol) lighter wiring that is built in to our vehicles is very tiny. There are (2) main things to think about in regards to wiring for our fridges. Now, you could still run the same amount of amps through various size (gauge) wires, but the smaller the wire, the hotter it gets. I'm pretty sure that the wiring for our cigarrete outlets is fine for our fridges. The second issue (and probably more important) is voltage drop. Lets say you have a 12v battery. You want to run a device that is located 10 feet away from the battery. You must run a 10 foot cable. Now... there are tables online out there that you can reference for the exact specs (I'm not going to reference any specific wire gauge size but I have looked at these tables many times), but to keep this short, if you use a skinny/small wire and run it 10 feet, the voltage at the end of the wire might be down to say 11.5 volts. If you run a thick/large wire, the voltage at the end might only be down to say 11.9 volts. You get less voltage drop with the thicker gauge wiring.
The reason this is important for our fridges is that they have a power shutoff feature that will shut the fridge off if the battery gets too low. Now, lets say the fridge thinks the batter is too low when the battery gets down to 11.5 volts. Well, the fridge might see 11.5 volts at the end of the wire due to the thinner wiring even though the battery might be close to 12 volts. This will cause it to shut off a lot earlier than you want it to.
If you want to have some fun, take your volt meter and test the voltage on your battery (with the engine off). Then test your cigarrete (there goes that spelling again... that just looks incorrect) lighter up front. Then test the cigarret lighter in the back. I guarantee you'll see lower results the farther from your battery you get.
Ok... Gotta get back to work.