Ok I will take a GUESS, and I stress this is a GUESS so if I am wrong, your FREE is cheerfully refunded.
You have an inverter that powers the TVs (And perhaps other things) at least THAT TV, when you are not on shore power or running the genrator.
When you unplug there is a brief "Blip" as it were in the power feed to that tv as the transfer relay in the inverter.. Transfers.
Modern TV's are computers.. Very powerful Digital computers.. now in the old analog days everything was "Hard wired" so there was no program running to speak of But with today's Digital wide screen HD sets.. The computer may be sensistive to that blip.. Just like a desktop can be reset by such a blip.
No solution that I know of other than turn off inverter.