I had a problem with my pickup that sounds exactly like yours. I am playing an Ibanez JS1000 with a Dimarzio PAF Pro humbucker for the neck pickup. I bought the guitar used and the neck pickup was always intermittent - it would only kick in if I took an allen wrench and touched one of the metal poles on the pickup. I thought it might have been a grounding issue but that wasn't the case for me. After checking all the solder connections I determined the pickup just needed to be replaced. I was surprised to learn that pickups aren't all that expensive and doing solder work really isn't too bad. I had a new pickup installed in less than an hour and everything sounded great.

I would take JEkade's advice and take it to a professional in your area just to get another opinion. If you decide you need to replace the pickup and are going to do it yourself, I can point you in the direction of some really great tutorials on youtube that helped me get the job done.

Let us know what you find out and good luck!