Random logoffs and a shutdown

Hi,

So I am using my Macbook Air and it would randomly blank screen and return to the login screen. This would be on a very low resource task such as browsing the web. I have MemoryKeeper and it is showing a sufficient amount of memory when these instances occur.

After one instance, my computer turned itself off a few minutes after. I tried to turn it back on to no avail. It required myself spamming the power button to get it to turn back on again several minutes later. This Macbook Air is less than 2 months old and is brand new.

I have called AppleCare and run through a couple steps deleting preference files and such. It hasn't happened since, although I haven't used it much since that occurance however. Not long enough to deduce the problem to be solved.

Any ideas why this could have been happening?