Xantrex specs cables on the heavy side to be sure, as they recommend cable size to match max current specs. In your case, cable size is definitely not the issue. The load created by your A/C is nowhere near the max amperage capacity of 2/0 wire. The cables would not be overtaxed unless you were running the A/C and microwave simultaneously, and even then, I don’t think you would exceed 2/0 ampacity rating. If taxed, the cables would get hot. For years, I ran my soft-start equipped 13.5K Dometic Brisk on my Xantrex XC2000w inverter/charger over 1/0 cables. I would agree with the Xantrex rep who suggested that maybe your cables are loose. An actual load great enough to tax the Xantrex input circuit would trip the fuse or breaker protecting the circuit (if you have one). If you can replicate the scenario, try putting a clamp ammeter around the positive Xantrex dc input cable. If dc current input fluctuates during this test, there’s a problem with your battery connection.
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Jim. Former, 2021b Micro Minnie 2108DS
Medically grounded, but still lurking the Micro Minnie Discussions
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