Is it just in the middle position with one (either) volume turned down that you get no sound? In the neck and bridge positions do the respective pickups work correctly? The standard LP style wiring has linked volumes, that is when in the middle position turning down either volume with mute all sound. This is normal and expected behavior.

If you want independent volumes, like on a jazz bass, where you can turn down either volume without muting both, it is possible but it will alter the sound slightly due to the different way the volumes interact.

Or am I misreading your issue?