I have the same problem. I'm playing through steam link with two steam controllers. The game only works with controllers which are turned on at the moment the game starts. If I decide to coop, and turn on a second controller, it won't be recognized, so if I want to coop the only way is if I turn on both controllers before starting the game. If a controller turns off for any reason (inactivity, low battery, controller gets too far from the steam link) there is no way to reconnect it other than restarting the whole game. If the main controller is disconnected, I can only save the game from the PC (using keyboard and mouse) before restarting, to be able to continue where I left. This is a 100% reproducible thing, I can never reconnect any controller. If I can help fixing this issue let me know, I can also run the analysis tool. It would be great to see this resolved, it is a super annoying thing, as the restart of the game takes several minutes (at least on my system)