I'm not a fan of all active basses. I do however love passive pickups thru a preamp. I've played basses whose electronics are configured this way for years. I play a lot during the day. My basses are plugged in ALL day. And, I leave them plugged in on my shows the whole time. I play a lot. But my batteries last months. I change em every 6 months, but they usually don't need it. Batteries I take out of my bass used I put in my tuner pedal. And it works for about another month or two. Way back, when active electronics we're first conceived and constructed, battery drain was a huge consideration. Today, with better, smaller parts, battery consumption has lessened. The voltage needed to power the preamp has reduced. And most preamps offer a ton of hours plugged in. I still unplug my basses when I'm not home, overnight while sleeping, etc. But generally, my basses are plugged in for hours a day. And I get months out of them. I would suspect a wiring issue if a battery died in a month. That could be the issue here.