I've checked the BIOS and there aren't any options that would cause it to switch off. The CPU/GFX/HDD/case temps are also fine. I haven't a spare PSU and I don't know anyone that could loan me one either.
I'm testing it with the MSI RD480 Neo2 motherboard and I have the 24-pin and 8-pin connectors plugged in and a molex also plugged into the motherboard. With the MSI Neo4-F I used the 24-pin and the 4-pin connectors.
It just switched itself off again after sitting idle for about 20 minutes at the desktop.
I could test it in my old system although it doesn't require a powerful PSU so it might not exhibit the same problems. I'll give it a try anyway.