I’ve got the jazz elite and I always unplug when not using it, this is from the fender owners manual,
Fender® offers basses with passive electronics (no batteries) and basses with active (battery-powered) preamps. Depending on
the instrument, your active bass may have either a 9-volt (one-battery) system, or
an 18-volt (two-battery) system. Visit the Knowledge Base in the Support section of www.fender.com, where the service diagrams link presents detailed information on more than 250 Fender instrument models.
Typical battery life for both systems is approximately 600 hours of playing time.
All Fender basses with active preamps are equipped with switching jacks that engage the battery when a cable is plugged into the jack. To maximize battery life, unplug your cable from the bass when not playing the instrument.