Controller getting disconnected should not kick you out of game

I'm using a DualShock 4 controller. I have a problem with the cable where if it moves, it gets disconnected from the game. That's on me, I need to fix that.

What doesn't make sense is that if a controller gets disconnected, the game should not log you out of the game, resulting in lost progress if running maps (or in my case, ultimatum). Please make it so that the game automatically pauses or switches to another control method if it detects a lost connection.