9v batteries are actually comprised of 6 AAAA batteries inside a rectangular casing. You can have a 9v battery where the internal AAAA batteries are leaking, but fail to permeate the metallic casing. Ever have a 9v that looks overly fat/distended? Yup, it's leaking internally.

I suppose that's why they recommend such frequent replacement. You could have a failure inside the battery and not even notice it because of the battery's external case shielding the problem.

Interestingly, all the new battery operated smoke detectors I've seen now use AA batteries. Thankfully, I gave up on battery powered smoke and CO detectors years ago and just had them all hard wired into the alarm system. Now I've only got one battery to change...the backup battery down the basement....which supposedly has a 10 year lifespan (though I change it out every 5 or so).