This sounds like a really weird situation.
I would wire the neck pickup to the bridge pickup's volume control (and disconnect the bridge pickup temporarily) to make sure it's not the pickup that is the problem. If the volume control then works normally I would swap the neck tone pot with the neck volume pot and see if that works. If the problem persists with the pot when it's wired as a tone pot, change it - it is probably defective then.
Cheers Stephan