Nope, not the power supply. Nope, not the proxy being used. Nope, not the pool being used. Nope, not the color tshirt I was wearing. Nor the phase of the moon.
It was the damned fan.
Even while it seemed to be moving plenty of air, it appears that the auto-shutoff circuit in the cube is based on how much current the fan is pulling. This is why when the fan was just starting to go bad, the stupid baffle trick worked. I should have thought of replacing the fan then, it seems so obvious now... ah well.
I replaced the fan with a 120mm 2200RPM 80CFM unit (cost me $5), and suddenly everything works just fine again.
http://www.tigerdirect.com/applications/searchtools/item-details.asp?EdpNo=8208359My beleaguered cube is now happily hashing away in the high clock speed (where before it would immediately shut off if I even attempted to overclock it).
In summary; if you have a working cube that suddenly starts turning itself off, replace the fan -- even if the fan appears to be moving plenty of air at first glance.