It does seem like a power cord issue. Occams' Razor: simplest explanation is usually the best. Among other things, you might want to seriously consider investing in a relatively cheap (~$100) UPS (Uninterruptible Power Supply) and plug that into your wall outlet, and your Mac into the UPS. That way, a bad wall outlet would be seen by the UPS (beeping when power was cut out), not by your Mac. Plus, a UPS is always a good idea for delicate electronic equipment. One just probably saved my G5 when it detected 150V in my power due to a faulty substation regulator - a surge protector won't notice "small" hikes like that, esp. if they don't come as spikes but instead ramp up, nor will a surge protecter protect you from or warn you about brownouts - voltage sags.
Of course, you might very well know all of this and already have it plugged into a UPS.
Still, I'd recommend, as above, checking the bottom of it (minus the plate) to ensure RAM and/or Airport are secure (mainly RAM). Probably won't help, but can't hurt - just ground yourself first (electrically, not philosophically). Then snugly plug it in. Good luck - and, as others have said, keep us up to date!
Edit: changed my mind. Loose Airport won't cause a shutdown, nor will loose RAM. Checking it might risk damaging it, and probably won't help. Again, if you have AppleCare, you might want to call Apple Support. Otherwise. I'd check the power cord. Besides a loose plug, it's possible there's a short in the cord. Look for cord damage....