I'm not all that familiar with the IIvx/IIvi/P600, but if the power supply is similar to the IIcx/IIci/Quadra 700 (all three of which I am very familiar with) I will advise to have a spare on hand at all times. Of all the early Mac power supplies aside from the Plus and earlier, this one has to be the most problematic. I've had similar problems with the computer randomly shutting off on my IIci, which was fine once I replaced the power supply unit.
I also once worked on a IIcx that wouldn't turn on. I had forgotten to unplug it (I was repairing several Macs that day at one time) and a few hours later it chimed on for no reason. Ah, the wonder of these old power supplies.
The P600, IIvx, and other machines of the form factor seem to have a different supply overall. You can buy one from Herb Johnson for $29 plus shipping (http://www.retrotechnology.com/herbs_stuff/m_parts.html#power). The P600 isn't explicitly listed, but keep in mind its corporate cousin is the IIvx, so any part for a IIvx will generally work with it.
I also once worked on a IIcx that wouldn't turn on. I had forgotten to unplug it (I was repairing several Macs that day at one time) and a few hours later it chimed on for no reason. Ah, the wonder of these old power supplies.
The P600, IIvx, and other machines of the form factor seem to have a different supply overall. You can buy one from Herb Johnson for $29 plus shipping (http://www.retrotechnology.com/herbs_stuff/m_parts.html#power). The P600 isn't explicitly listed, but keep in mind its corporate cousin is the IIvx, so any part for a IIvx will generally work with it.