That sounds SO much like a loose wire somewhere on the AC side and a good place to start is the ATS. These are rock and roll houses.....
However first check the power pole from the campground, these receptacles are known to wear quickly and a simple bump of the power connector could cause what you are describing. Have you been connected to the same pole over the last 10 days?
If you can, grab some of the wires one by one where they come out of the ATS and the distribution box (not inside the electrical box) and just pull and push then a little bit. If you duplicate the problem then you know where to look.
The inverter.... any power burp will cause it to reevaluate the battery charge and it's status, after a few minutes should return to normal.
Troubleshooting is always a process of eliminating what is working to fine what is not..... Good luck.
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