I received my new MB June 26 and after just one day of heavy use, it did the random shut off. I too had the same pattern described by countless (well, I'm sure someone will eventually count us) others. It would shut down randomly, then I would have trouble turning it back on for a few seconds. Then after I would get it back on, it would commence to turn off randomly over the next hour after anywhere from 5 seconds to 5 minutes (I used my stop watch). After this first round of shutdowns, it didn't do it again until a week later and again, I had a little trouble rebooting. It has only done it once more, yesterday. I took it to a Mac Store and they claimed its not a known problem by Apple and that they would deal with it as an individual problem.
Now, I absolutely love my computer (I've had some previous academic Apple use but have owned a Dell laptop for last 5 years). I think it looks great, the programs are first rate, the functionality and design of the computer and everything about it are just awesome. So if there is a fix, I'll happily wait a couple of weeks with my unit in the shop.
Unfortunately, I don't want this to become an open ended problem that I can't recreate. Hopefully, either it won't happen again, or will happen so frequently that Apple can diagnose it and fix it. I start school Sept. 20 and would sure like to have this taken care of by then. It sounds like until it happens so frequently that an Apple tech can see it, not much you can do if you're past the first 14 days. I don't enjoy this feeling of powerlessness. However, given all the positive feedback on Apple Care, I'll call them this weekend and start talking to them about it. Also, I really appreciate this forum to let folks know they are not alone or crazy. It's not you, it's your computer.
Regarding the quote below, perhaps Apple should embrace the random shutdowns and offer it as an exciting feature, much like for the shuffle: "Life is Random, when will YOUR MacBook shut down?"
"Your toaster doesn’t crash. Your kitchen sink
doesn’t crash. Why should your computer? Think of the
countless hours you would save if your PC worked on
your time — not the other way around. Then think
about a Mac."
MacBook Mac OS X (10.4.7) 1.83GHz, 1MB RAM (Apple installed), 80GB HD