At first I was thinking your power supply was going but the fact you can leave the system running and only during a set point in the installer it fails leads me to believe the issue is either a failing RAM module and/or your CPU is over heating going into thermal shutdown.
Fixing the RAM is the easiest to do. If your system is overheating then you'll need to start off by doing a full dust clean out (fans & logic board). I would also clean and re-paste both the CPU & GPU chip heat sinks and do a full inspection of the the heat sink heat pipes you might have a bad unit.