It's a good chance its your PSU.

When everything is under load your computer probably draws peak wattage of your PSU so 600 Watts. The problem with that is that PSU's technically don't draw 600 Watts from the power socket, they draw a variable amount to supply 600 watts to the computer. So if you're not able to draw enough from the wall socket that could create an influx into your PSU so if your computer needed 590 watts to run under its current load but were only able to get 589 W theoretically from the wall then it would cause a shut down.

http://www.howtogeek.com/129667/what...ply-unit-mean/

I've had the same problem with a 550 W PSU, it wasn't enough. I upgraded to 750-800 W just to be on the safe side. I would suggest replacing your PSU to at least 650, 700 to be safe. Other's may disagree, but that's my opinion based on my own experiences.