Active pickups or active EQ circuit? They'll act differently depending on what the actual circuit is. Since I started using active instruments in '79, I've only had one battery issue (the only time I didn't use a Duracell- the "Ever" ready wasn't ready...). They symptom on a pre EB StingRay was distortion, much like a bad solid-state overdrive. Same gain level, but distorted signal.
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"Without space, music is just noise piling up on itself." TRK
"Don't play your instrument, play music." Feral Feline
Lakland Owners' Club #248