[Fulltiming]

If your inverter relay is operating properly, it should switch fast enough that most electronic devices will not notice the difference, at least it does on my sine wave inverter. When you lose 120 volt at the pedestal is there a switching delay or does it just not switch over to using battery power at all? You could try unplugging the remote at the inverter and controlling the inverter directly from the inverter to see if that solves the problem. That would isolate the problem to just the remote.