When I upended my computer to look for the EMC code, I noticed that the round vent hole above the power cord was PLUGGED with fine dark grey dust!!! I sensed that the computer was heating up rapidly and thought that might have something to do with the sleep condition.

Lo-tech solution: I took out the vacuum cleaner, sucked all the dust out of every nook and cranny. The computer hasn't unexpectedly gone to sleep since!!! It's been 4 days. I think it's cured it of its narcoleptic fits.

Thanks for all your input, nonetheless. Hopefully this is the end of this thread.