I take this is the first time you've tried recording this guitar? I don't have a lot of practical experience with active guitars, but any active circuit necessarily has its output limited to something less than the power supply voltage. If the input from the pickups times the gain of the circuit is greater than that limit... Depending on a whole bunch of things, it is possible to clip it even with a brand new battery. If that's what's happening, you need to either reduce that input from the pickups or reduce the gain of the circuit.
It's not likely that you can reduce the gain without a bunch of fucking around. Usually those things have some set amount of gain and a passive V knob on one side or the other.
Reducing the input from the pickups could be as easy as turning that V knob if the pot comes before the active circuit. Otherwise, I think, all you can do is lower the pickup away from the strings a bit.
Edit - Course, it's possible that's just how the thing sounds. Most electric guitars sound pretty crappy straight of the pickups without some shaping from the tone controls on the amp and the bandwidth limitations of the speaker. A bit of EQ and/or compression or a good amp sim could just fix it, but I'd still want to make sure the guitar itself is doing the best it can first.