A run of "X" feet (long distance) from batteries to inverter...
E=MC2 told you X gauge wire would work fine and it did. Then trouble arrived. You suspect the cables or a connection. Clamp the carbon pile wires onto the shut off inverter's connectors right over top the cable lugs. Twist the CP load knob to your theoretical E=MC2 amperage value and watch the volt gauge. Oooooooo, it's sagging way down. STOP! OR YOU'LL HAVE A FIRE! Unload the carbon pile and quickly start checking connections with your hand.
Properly sized and constructed electrical conductors DO NOT GET WARM. EVER. This testing is valid on a solar panel run and ANY OTHER amperage bearing power wire. Those wires are intended to pass a specific current. If they can not do that then you have a problem.
Even a marginally "bad" connection will heat up dramatically. Sometimes you'll need a helper on smaller wires but keep repeating the load draw and go down the line.
While some techs are still scratching their --- I have finished my repair and am on my way home.load testing cables is easy, with dramatic results and is infallible. I do not use the word infallible lightly.
Pssttt Sizzle Sizzle (obscenities) sure found that impossible-to-find bad place in a hurry, didn't you? Warm places are disasters waiting to happen.