From your description of the problem I gather that the trigger is supposed to send a keycommand via the Logitech Profiler? From my experience with the Profiler, it sometimes does not apply the profile properly. I believe there are some options wrt applying that you could experiment with. It might also help to make a profile for notepad to check that everything is working ok, or use a key testing utility. There may also be some issues with changes to a profile not being noticed if a fixed profile is used.
If at all possible, I would try to map the joystick button in FSX directly instead of using the abominable Logitech Profiler.
Good luck with this, I hope you can get it to work.