Low power from 12 volt outlets

Hi everyone, I'm having an issue with the 12 volt outlets (cigarette lighters) in my RV. It's a new-to-us 2004 Colorado 5th wheel, but we haven't used the 12 volt outlets until today.

In our last rig I had an inverter that powered the whole rig, but with this one I wanted to save money so I got two Bestek 400 watt inverters.

The problem is that devices powered off the inverter are getting intermittent power. The TV is 85 watts and keeps powering off. My wife's laptop is like 75 watts and it charges on and off. I can hear the inverters revving up and down, and occasionally the power/fault light turns red then immediately recovers.

I checked the voltage from both 12 volt outlets and they are fluctuating between 107 and 115 volts.

The fluctuating voltage is obviously the problem, but I'm not sure why. We have four 6 volt GC batteries and AFAIK they are fine. I check them regularly. All other 12 volt systems in the rig work properly.

We have friends using this same 400 watt inverter and they do not have this problem.

Could it be that the fuses are too old? Or the outlets are just bad? Any feedback is appreciated.

Edit: I fired up the generator and the problem persists. With the gen going the 12 volt systems should be pulling from the shore power through the converter, right?

Thanks!