My guess is your output jack is wired incorrectly. When wired correctly and used with a mono plug the stereo jack acts as a battery defeat, so the battery is physically disconnected when nothing is plugged in. If the cable is left plugged in to the output jack, then your battery is constantly draining, even if wired correctly.
And yes, the nature of the buffer circuit is such that when no power is supplied, there is no output. Your guitar can be wired to switch between passive(non-buffered, no battery required) and active(buffered).