Brian:
Read your post on CPF and need more info as I know nothing about Arc lights in particular but have dealt with mechanical things of all types most of my life.
I have a Maglight Solitare on my keychain with a twist CCW to turn on and tighten CW to turn off the light. The switch is a pressure sensitive membrane surrounding the perimeter of the bulb and its mounting holes.
If the Arc works in a similar fashion, I would look at the possibility of dirt not allowing the membrane switch to close, or bad engineering on the cap that does not have a deep enough flange in the caps interior to push on the membrane switch. The worst case scenerio would be a cheap contact material used in the membrane switch which is oxidizing.
If you get an answer that works, let me know how close I was to being correct.
Good luck!
Bountyhunter