I use a 2300mAh high capacity battery to power my AP. See:
http://www.ardrone-flyers.com/forum/vie ... 589#p10589
Have been using this for most of my outdoor flights now and I connected the battery meter only a few time until I realize that this battery will last for quite a while.
I didn't do any measurements but looking at the brightness of my battery meter LED display, it may draw as much power as the AP itself if the meter is left connected all the time (Just kidding but may not be that far off). I usually measure the battery voltage before every flying session just to be safe. As long the voltage is over 11 volts, it should be ok. I'm sure there are alarm circuits out there you can rig up easily for your AP supply since weight is not that critical.
With that said, I must stress that I am using a regular consumer run of the mill AP which draws a lot less power than a high powered 1000mW or more AP. Since I mount my iTouch on top of the AP and use it as one unit, I want to have a small battery pack. But if your AP is at a fixed location, there are lot of battery options you can consider.