battery runs out - computer doesn't go to sleep

Pismo, check your system profiler in About this Mac > More Info > Power. I don't know if that is exactly what it is called with Snow Leopard but there ought to be battery diagnostic information buried in there somewhere.

Copy and paste it here.

I'm wondering if your battery is on the verge of failing.

OK, that AHT code is normal when the power cord is NOT connected: http://support.apple.com/kb/TS3578

It looks like your battery is just fine also.

Try this: Reset the System Management Controller. Reasons for doing that are many but include the following (bold emphasis added):

Power

The computer doesn't respond to the power button when pressed.

A portable Mac doesn't appear to respond properly when you close or open the lid.

The computer sleeps or shuts down unexpectedly.

Intel-based Macs: Resetting the System Management Controller (SMC)

On the MBA, the procedure is as follows:

1. Shut down the computer.
2. Plug in the MagSafe power adapter to a power source, connecting it to the Mac if its not already connected.
3. On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
4. Release all the keys and the power button at the same time.
5. Press the power button to turn on the computer.
   Note: The LED on the MagSafe power adapter may change states or temporarily turn off when you reset the SMC.

Post back with your results.

This could be because (as a preference) the sleep mode has been changed from Safe Sleep to something else.

cf: http://macs.about.com/od/usingyourmac/qt/Change-How-Your-Mac-Sleeps-Pick-The-Sle ep-Setting-You-Want-Your-Mac-To-Use.htm

To quote from that article:

When the Terminal window opens, enter the following at the prompt:

pmset -g | grep hibernatemode

You should see one of the following responses:

hibernatemode 0

hibernatemode 1

hibernatemode 3

Zero means normal sleep and is the default for desktops; 1 means hibernate mode and is the default for older portables;
3 means safe sleep and is the default for portables made after 2005

I was having the problem you are describing on a Macbook Air. When I ran that command in Terminal, it said I was in `hibernatemode 0`

To fix it, I entered this command, then enter, then my password.

sudo pmset -a hibernatemode 3