The client just disappears without warning? No black screen, no pop up about drivers being outdated? Are you playing with the most updated version of Minecraft (1.3.2, I think)? Is it a legimate copy purchased directly from the Minecraft site?

The only issues I've had with Minecraft were some blacks screen problems that were solved fairly quickly. Never had a shutdown, though I'm sure they happen. You should check the forums to see if you can find any problems similar to yours.