hi i had the same problem. if you have not found a solution yet here you go. I found this on the BIS forums posted by user jjrmed:(https://forums.bohemia.net/forums/topic/204689-joystick-detection-problem/?tab=comments#comment-3189235) Post#4
I might have found the problem and a solution. Nomylol, were you using steam's big picture for other games that need a controller? In my case I had a generic controller added to play rocket league. Turns out that turning off xbox, ps4 and generic controller support can lead to the Joystick being visible again for Arma 3.
I had done exactly that since I play rocket league. I went into Steam Big Picture Mode went to settings -> controller settings and unchecked Playstation configuration support and generic gamepad configuration support.
Basically I unchecked all except for "Guide button focuses steam"
after that just restart arma (I restarted Steam too just in case) and all my controllers showed up again.
hope this helps you too.