hey dude...
I had this exact problem with my baby... Only I was using it to light a smoke... I don't understand the hype about neons really... but hey thats just me...
anyhoo, I found the problem to be the contacts in the chamber. If you look inside, there are two prong things (don't know what they are called) and they are easily bent too far back and not making contact with the device you are trying to plug in. just bend them back in towards the centre and see if that works.
If it doesn't, it could be the conection at the back of the lighter. it is pretty simple to check, the chamber simply unscrews from the facia and the wiring is connected onto what can only be described as a screw. Make sure that it is connected properly and not corroded at all and spray it with some electrical lube (air based aerosol, able to be bought from any hardware or electrical store), clean it with a wire brush and re-connect it. screw it back in and see how that goes.
good luck
why is monosylabic such a big word???