Eek! A mouse

I just changed the batteries in my cordless mouse for the umpteenth time in six months. Why do I have to change it so often? Do the batteries stay in use whenever the computer is on? If I turn the computer off, will that conserve battery power in the mouse? This is pretty annoying. I like the cordless mouse but hate the battery changes. Guess I should hunt down my rechargeables, but where could they be? Probably under a pile of makeup! *sigh*