I change the batteries in my active basses once a year. That's been my practice since my first active bass, an Music Man StingRay I got in 1978 or early '79. The only time I've ever had a battery issue with any of my active instruments was that StingRay the one time I used an EverReady alkaline. Going back to Duracells and I've not ever had a problem with annual changes. That's experience with two pre EB StingRays (that did NOT have the switching jacks), two Guild Pilots (one regular, one Pro with an internal pre-amp in addition to the two EMG active PUPS), two US Lakland 4-94s, a Skyline 55-01, a DeArmond Ashbory, and my fretless which has a Duncan/Basslines Steve Bailey pre-amp in it.
Less than 6 months and I'd be getting things looked at- most active circuits in basses just aren't that high of a current draw. Of course if you're using rechargables (which are never 9 VDC when "fully charged" or regular carbon/zinc batteries you're gonna go through them faster.
jte