I've just found the most annoying dead-spot on any bass guitar. While most Fenders have it around the high C (first string, fifth fret), this brand-new Epiphone Thunderbird active 5-string has an enormous dead-note area: from the open low-B on the 5th string to the fourth fret of the fourth string (G#).
I have to say this guy is not a newbie. He owns three other basses, is a semi-pro, and tried lots of things before asking me for help. He's used three sets of strings, with different gauges, different tunings, and even inverted the nut to string it up lefty-style. The dead spots have always been there: from the low-G# and downwards.
Usually, adding mass on the neck shifts the dead spot to a lower note and gives more sustain (Billy Sheehan has been using a C-clamp on his Yamaha for decades), but I doubt it could be useful in this bass. I mean, it's a Thunderbird: the shit is one of the heaviest basses around! And its neck-through-body 7-piece maple/walnut neck is supposed to increase rigidity and a more even tone.
I don't think that other pickups can solve the problem, because it's still noticeable when unplugged. Maybe installing steel or graphite reinforcements in the neck can increase its rigidity, but it's hard to spend that kind of money in a $600 instrument.
That wide-frequency a dead spot is sure alarming. I'll assume pickups are not to close to the string and that the bridge is tightly screwed on the bass. You can make a test with "supersteps" or "longnecks" strings too.
As far as I know frequency dependent problems (I'm a former mechanical engineer), it seems weird to me. My first try would be to mount a passive pickup put on U shaped piece of wood, double sided taped to the body, upside down (top of the pickup facing the strings, bottom taped onto the wood). That way, you'll be sure that the "dead spot" is not a "too compressed bass response" coming from the active electronic part of the system. It sure happens often on basses with that quality level and make you believe the lower notes are dead. Which is, most of the time, wrong. If the temporary pickups sings, you know what to do : upgrade any active part of the system (i;e; EQ and/or pickups).
If that test demonstrates it does not come from the electronics, then, I would try to listen to the unplugged bass with a stethoscope : it helps to be sure the problems come from bass itself. If you hear the dead spot with the stethoscope too... I don't think you can do much, apart from what has already been done.
Paul is right : if the instrument is new, use the warranty. If not, then my first answer applies!
If it's brand new, he should exercise the warranty and demand a different instrument.
I think if more folks would take advantage of "warranties", the manufacturers would get better feedback on their products.
You probably know that Thunderbird style basses have a reputation for having the most "unbalanced" responses in the world.
They're historically bottom heavy and "thuddy". What you're describing is the classic "problem" with these styles of basses.
And (I'm sure you know this too), $600 street for a bass is considered "lower end" just above 'budget grade' instruments.
Has he tried using a compressor? That may help.
Best of luck & I hope someone can give you some great advice on correcting this.
Again, I'd simply request a new instrument, and KEEP requesting until he finds one that performs to his expectations.