What is causing my Advent 7101 laptop to shut down suddenly?

If it's anything like my Advent 7011 then it's probably overheating - it's designed to do it. It's a really stupid setup, it has the air intake in the bottom where it can't really get any air and the heatsink is too small and the fan is too feeble. You should check that the heatsink is clean and that it's airflow unobstructed. I have to prop mine up on two books in the summer and not get it to work flat out.