The pre-amp in the guitar is switched on by the insertion of the jack plug, The jack socket uses the barrel of the jack plug as a shorting circuit which bridges the sleeve and the ring, allowing the battery to feed power to the pre-amp. Remove the jack plug and this short no longer exists, so the pre-amp no longer receives voltage, and the battery can rest until the next time. If the jack is left too long in the socket, the battery is drained, which is why one has to unplug the jack when putting the guitar away.
There is no good reason that I can think of for using stereo (RTS...) jacks for guitar or bass, and for those with a pre-amp (your electro-acoustic...), this switching function is defeated, as there is no short-circuit created between the sleeve and the ring. Use a mono jack, as one should with all guitars and basses, and all will be well. You've just been lucky so far that stereo jacks work at all, as they are far from optimum in mono jack sockets. Hope this helps.
Douglas