I'm the second person with this problem I've heard of (Snafu's cousin experiencing the same anomoly)
The computer will suddenly not recognize the Joystick (usually while in flight, in the middle of a good fight, Murphys Law) and the lights go off on the stick. Work around is hit autopilot, unplug USB, plug it back in, reload profile. I can do this all in about 30-45 seconds if I'm really fast.
I tried uninstalling and re-installing latest drivers, etc.