You may have a cooling problem. When you run on the battery, it is no-doubt running on a lower power setting. You could try changing your power settings to run much leaner when on AC power. Then you can see if it still shuts down on AC. Obviously, cleaning the fan would be a good idea. You might want to get this fan utility:
http://www.diefer.de/i8kfan/
chrishea
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