Active pickups ALWAYS require batteries that work. Whenever a cable is plugged into the output jack, the battery is powering the pickups. I've had batteries last six months or more, but it depends on how much you play it and whether you forget to unplug it from time to time.
When the battery starts to go, you'll start to "fight" the guitar to play how you like it. It will sound weak and maybe a little fuzzy, and you'll wonder why you keep fucking up, until you realize that probably means you need a new battery.
Know about how long your battery lasts before you start using an active-pickup guitar for gigs, or else you should probably swap out the battery before the first gig, and at least every month thereafter - you don't want your battery to die mid-gig.