1. Does it run without the battery? (if so, battery is dead or shorting out)
2. AC adapter could be going out or not working properly. I have people do this at work, they run and run on battery not knowing the power pack or outlet isn't working, they have been running on battery for hours and it eventually just shuts down on them.
3. Could be a short in the cord of the power pack, you think its working, but it might not be depending on if the cord is touched or moved.
4. Hard drive might be over heating. Does the laptop seem to run ok or is it acting slow? Laptop drives tend to go bad more frequently than desktop drives due to size, heat and space inside those laptops. If the drive is failing and working extra hard to read the data, it builds up more heat and will shut down.
5. Is the laptop sitting on a docking station or stand alone?
6. Is the laptop on your lap sitting on something soft like pants or blanket that will be blocking the cooling ports on the side or bottom of the unit, causing excess heat build up.

what brand of laptop?