Pickup not...um...picking up

I've been having this problem with my Esquire for a while. Every so often, the pickup just goes dead. It does pick up a very small amount of sound, but at least one switch position is completely silent; the other two make a tiny bit of noise. Leaving it for a while usually fixes it, though I can't say how long I have to leave it (it varies).

I thought it was wiring at first, but I've checked it and it seemed ok. In frustration, I tried adjusting the pickup height.

Then I accidentally tapped one of the magnetic poles with my magnetic screwdrivers and...BAM! Noise again. Could this be a grounding issue or something like that?

Sorry, ignore that. I've been adjusting the pickup height and it cuts out when I try to adjust the screw under the highest-pitched strings. :(

Shorted winding?

Would that cause the intermittent problem, or completely kill the pickup?

I've been experimenting, and found there are certain heights where the pickup stops responding. Also, there's a point where I can keep unscrewing the screw but the pickup doesn't sink...the screw starts pushing itself up, as if something under the pickup is stopping it (the wiring I'm guessing; I've had a look under the bridge plate and there's nothing else that could obstruct it).

If it was a problem with the winding, would that be repairable or would I need a new pickup?
Cheers :)