I have this issue, or something like it, quite frequently. If for any reason the connection between my controller and the computer drops, like the cable is starting to wear or it gets knocked out of position a bit, then the game refuses to recognize the controller again until I restart. If I’m “lucky,” I just have to restart the game. If I’m not, I have to restart the whole computer.
Meanwhile, other games have no problem immediately recognizing the controller again even in the middle of the game. Skyrim, Fallout (4 and 76), Mass Effect, Dragon Age, even LEGO games don’t have any trouble. It’s just ESO (that I know of) that refuses to recognize the controller again if it loses connection for a moment.