Using ATX PSU as stand-alone power supply: PSU doesn't stay on longer than ~1 second
The problem was that I shorted PS_ON to ground without the cables connected to the power supply (it is a modular PSU). The voltage sense wires were not connected to their corresponding partner because the cable was not in place. Hence, the PSU thought the voltage was off and shutdown. 

The solution was to look at the pinout, and see which +3.3, +5, +12, and ground pins overlapped on the ATX cable. I shorted those to each other (+3.3 &lt;-> +3.3, +5 &lt;-> +5, etc) and now it works great!