We may have covered this before, but Mrs Heathen was wondering “how long will the power last in the event of a catastrophic mankind-eliminating event?”
Well, this is awful close to Straight Dope’s answer to “When the zombies take over, how long ’til the electricity fails?” Cecil covers both sudden and gradual zombification. Sadly, the answer in both cases is “not very long,” though obviously we do rather better in a gradual scenario. Coal plants require nearly constant activity to keep creating power[1], and they form a big chunk of the grid. Add to this the inter-relatedness of the whole affair, and you can see how the failure of a few coal-fired plants could bring down entire regions, if not more.
[1. Yes, we know they’re not “creating power.” They’re actually converting matter to energy. Shut up.]