First, use good batteries. Maybe new generation rechargables, but old type rechargables are death. That's because a fully charged battery rated at 9VDC is only about 8 VDC, and most circuits start to crap out when the voltage drops below 7.
Does active bass have a battery?
However, it will sound different and you won't be able to use the EQ controls on the bass itself. If your bass is only active and has no passive switch it will not work when it has no battery. In conclusion, the life of a battery in your active bass will depend on many things.
Does active/passive switch prevent battery drain while plugged in a bass?
If a bass has an active/passive switch it is guaranteed to have passive pickups (active/passive switches do not work with active pickups). With an active/passive switch, it may or may not prevent battery drain while the bass is plugged in. It depends on the bass. Hmm. I did not know that about bass pick ups.
Should I put a battery in my bass?
Of course, you could have gotten a battery that was in the bass longer, or played a lot at the store before you took it home, IDK, anything is possible with the battery that come with the bass, but if you put one in, it should not bother you for a while.
The cable still being plugged in was your big problem for sure, but always remember that not all batteries even of the same type/brand won't last the same. Depending on how long they have been sitting on the shelf, storage temp and factors like that, you might get 4 months from one and 6 from the next.