Hmm. The first thing that occurs to me is the pickup height, but it sounds like you've checked that.
Next is, always, to put a new battery in it. And then another new battery. Sounds crazy, but all of us have been caught out by either putting in a battery we thought was new but wasn't, or by a new battery that was actually dud.
If that doesn't resolve the problem, then I'd next worry about the pots. Does the volume control have the same range of travel as the other pots, and does the volume change throughout the range of the knob? I'm wondering if there's some dirt or something in the pot that's limiting the volume. Failing that, I'd look at all the solder joints. In fact I'd probably just re-solder all of them to be sure that they're good.
Are the pickups passive or active? Are they both the same volume? If not then it's reasonable to assume one is dying, but if they're both about the same volume then they're probably both fine.
Good luck!
