I recently had a bass assembled for me by an expert who's been doing this for me for about 25 years. I'll ask him about this, but I thought I'd ask here first, for more input.
The bass has an alder Squier body, a Mighty Mite neck (with maple fingerboard) and Fender Original Precision Bass pickups. The bridge is a '90s Fender string-though-body one. The tuners are Schallers.
My question is: The E string has a muted, dead tone.
It sounds that way acoustically, too.
It sounds that way with more than one set of strings. (I've used GHS Boomers and Dunlop Nickels on it. Identical gauges.)
It sounds that way whether I string the E string through the body, or through the top of the bridge.
The fretwork is beautiful, the nut is fine, and the other strings sound loud, with full harmonic content. The pickups are nice and low (the tops are about 1/4" above the face of the bass) and perfectly level (so the polepieces "assigned" to the E string are not any lower or higher than the others).
I'd like to keep this bass because it plays beautifully and the other strings sound great. But the E is a deal-breaker.
My guess is that there is something about the neck or body woods that is causing dampening, or low resonance. In that case, there's not much to do but replace one or both, or just sell the bass.