Ah, ok. I see you mean a momentary switch. I'm not familiar with the Arduino HID controller, but I guess it's similar to Leo Bodnar's BU0836A. When you use a momentary switch, in Windows game controlers screen you can see a button turn on. You let go of the switch and it goes off.
In some controllers (I use PHCC) you can specify a command when an input is On, and a different command when it goes Off. In BU0836 (And I guess Arduino HID, since you're having that problem) you can't do that.
You can, however, use software to do that. I've go to look in my bookmarks, but I remember at least two apps where you could write a scrip that e.g. sends a keyboard command when a joystick button goes on and a different when it goes off.
HTH