If they detect some kind of overload [current] it shuts the supply down. Sometimes it is only the inrush curent to drives/charging capacitiors the cause the shutdown. Have you added any hardware recently???.
Try disconnecting all of your drives [both signal and power cables] to see if the supply stays on. Then troubleshoot. Many other things can cause an overload, fried CPU, bad memory stick [if you have two, try one at a time. And, of course, the power supply itself can fail and shutdown erroneously.
AMD CPU's run hot as hades, so when you are in the computer be sure to first clean out all of the fans, dust balls, heat sinks et al.
The machine is a one year old AMD XP 2000. When I push the button to start, the LED lights on the front of the case blink and I can hear the fan start. Then everything shuts off, and pushing the button does nothing. I reset the 0 -- switch in the back of the case and tried to restart, but it does the same thing. I get a two or three second attempt at starting and then everythink shuts down.

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