I had trouble with my MacBook randomly shutting down too. I took it into the store and talked with a genius who immediately knew how to replicate it and shipped it off for repair for me that day. While it was being fixed they also noticed that there was slight discoloration on the plastic cover around the keyboard, so they replaced that as well. I didn’t pay a dime and had my laptop back to me as good as new within a weeks time.
Any computer can have problems, but what I have loved so much about Apple is the way they handle me as a customer.