What does your dash voltmeter indicate when this occurs.
With that large an inverter it is possible to overload an alternator, even a large one on your DP. I would start looking at what other loads are on that you are not aware of.
With the appliances you mention, there should be no problem. Also check for loose connections at the battery and inverter that could be causing the voltage drop.
If no extra loads and no poor connections, next step would be to stop when this occurs and use a digital voltmeter to check voltage AT THE INVERTER. That will tell you if it is an internal issue in the inverter.