Check in controller / stick mapping in the game and see if button 14 ( I'm pretty sure that's the one) has been mapped to something else
iirc, button 14 is the one that changes the stick through the modes unless I'm mixing it up with the CH pro throttle
You can go into windows/devices and right-click your controller/stick and see which button # it actually is
Edit: on the CH fighterstick the stick's button to change the stick modes is button# 3.... on the CH pro throttle it is button# 13.... <------ this has nothing to do with how you might have your 4 modes set up in-game...