Laptop is shutting down randomly, what could be the issue?

It sounds like your laptop may be overheating. This happens when the laptop components get too hot and turn off. It's pretty common for a vent to get blocked by something like dust, cutting off airflow. Try cleaning the vents on the laptop with something like a can of compressed air. That should allow more airflow, keeping things cooler and working.

If that doesn't work, then it could be a more serious issue. I would check out the troubleshooting page about that here.