I have to fight to keep humidity over 30% this time of year. If it sounds good when you put the new strings on it, I have a hard time thinking of anything that could be wrong with the bass that would repeatably cause it to sound dead after a few hours of new strings. If it were some number of hours after a battery change, you could look at the electronics. It just doesn't make sense. If the problem were in the bass, then it would never sound good.
I would delve a bit deeper into your problem description. Under 'normal' circumstances, would you dislike the tone of brand new DRs because they are too bright? If that sounds right, then it would explain the phenomenon because right when the strings are settling in to the way you would like them for months or play, they now appear too dead on that bass.
One thing to test would be to take the set of DRs off the Elan and fit them on one of your other basses to confirm that they sound good. That will rule extraordinarily bad luck with strings out.
Here's another thought - how does the bass sound unamplified? If you put your ear against the body or neck as you play, do the notes ring the way you would expect? If so, then you again want to look at the electronics. Alembic electronics are pretty modular, so you may be able to swap some components between your Elan and other Alembics, depending on what they are. I'd get help from Mica or Valentino before going that route unless you're really comfortable with it.
I might also try to plug in one of the other Alembics (minus strings) and hold it so that the pickups can read the Elan's strings while you play. I'm not sure if it will prove anything, but if it sounds pretty good, it might again point at the electronics. While you're at it, you could try the reverse and compare.
Does your problem care how you pan the pickups? If not, then they are probably okay and any electrical problem would be in the preamp section. Either way, you might try adjusting pickup heights up closer to the strings if there's room to do so. While you're playing with that, you might also see if you can bring up the pickup gain via the control pot insisde the electronics cavity.
Sorry, just a bunch of wild ideas to try to get more info about what could be wrong. There are probably more elegant ways to get this info, but I don't know them.
-Bob