You're going to hate me. My MBA is mid 2012, my wife's Macbook Pro is mid 2011.
Sorry for the mix up.
But I have good news for me, and hopefully for others.
When I bought my MBA (mid-2012) I got a free upgrade to Mountain Lion. The upgrade came about a month later, sometime in August 2012 I think. I upgraded directly to it. That's when I started having issues with the battery. The % charged would go down by 1% every minute or two until after around 3 or 3.5 hours the computer would shut off. This was with me running nothing but Safari, or nothing at all, and the cpu running normally, not spiked.
I tried lots of stuff suggested on this board, but nothing worked. So I reformatted my hard drive and installed a fresh version of Lion over the Internet. Everything went back to normal. That's a very short synopsis of my issue and how I worked around the "battery" issue (by giving up on ML.)
So this time, instead of doing an upgrade install, created a bootable SD card with ML on it (check out Youtube for some great instructions.) I then wiped my hard drive and did a full, fresh, clean, install of ML. Not an upgrade. Everything is running nice and fast. I let my MBA site for about 3 hours on the charger to let things settle.
Then I did the following to test:
I turned off power nap
I turned off the screen saver
I set the screen to never turn off
I turned off the "slightly dim" setting for when on battery power.
I turned off power nap
I then set the screen to 50% brightness
I then unplugged my MBA.
After about 2 hours it became obvious that everything was fine. I was right at 80% power, maybe 79 or 78%. I forget exactly because it was obvious I wasn't having the issue any more.
I've been using my "new" MBA, "ML Edition" this week and the power issue hasn't come back. Even after installing my apps again.
So, if you had the same, extreme, power issue. Try an SSD reformat and fresh install before giving up.
Woohoo!
Thanks for all the good posts!