I have been having the same problem and I called Applecare Yesterday and I was asked to try the PMU reset procedure and some more tests...nothing worked and at that time, it got worse and I had random shut down more than 10 times yesterday.
I brought it to Genius Bar today and gave my case number and also I told him that there are many people having the same problem (according to this board) and some people have their computer replaced. The guy at Genius Bar said he has never heard of this problem... and he turn my computer on and shut it down within 2 min...and said that I have to send it back...
I asked if I can get it replaced at Genius Bar but answer was NO.
So, now I'm waiting a box so I can send it back to fixed...( hopefully...)
But, right now, my computer is working fine.
I turn it on with AC pluged in last night around 9pm. I closed computer and it went sleep till this morning. Around 10am, I opened it and it was just fine. I turn it off around noon and brought it to Genious Bar and came back, turn it on around 3:30pm and till now, 6:45pm, no shut down...
I wish I don't need to send it back since I really need my computer with me, plus if Apple hasn't figured out what is causing this problem for sure, there will be a chance that my computer wouldn't be fixed totally.....what is the best for me to do...??