Two TVs use the same antenna, but one affects the other
It seems to me the problem is your antenna is only ever powered through the USB adapter at TV1, which is plugged into TV1.

If you turn off TV1, the USB port has no power and neither your antenna gets any power. The power adapter at TV2 is redundant. It can't power the antenna because there's no power pass through the power adapter plugged into TV1.

Power the antenna through a mains-USB adapter instead.