One of the my basses, Hohner Professional B Bass 5, the battery for the active lasts about 2 weeks. Any clue to what this could be? And how do I fix it? And no, I don't leave the instrument plugged in either. :)

Thanks in advance.

I'd be checking that the jack is wired correctly. The battery should disconnect when you unplug the bass - maybe that's not happening with yours.
Usually the preamp power supply is wired to the 'ring' connector on the input jack so that it connects to the 'shield' when a standard plug is inserted.