If the jack doesn’t work by itself or with the “all” buttons I’d say the issue is in the controller board and not with the keypad. The coiled phone cord sends codes down to the controller so very unlikely to just fail one jack. Also if the other 3 run when pressing the all up/down buttons that means the controller keypad is working and the issue is local to the controller board for that one jack output.
If it were mine, I’d open the control box and see if it’s something cheap like the $8 relay on my fridge’s control board.