Why does coffee taste awful after reheating it in a microwave oven?
It has nothing to do with the microwave and everything to do with the volatility of aromas and flavors in coffee. Even coffee kept warm for 4 hours won't taste very good. In my experience, stale brewed coffee results in a more pronounced acidity, if left out to cool, or a woody, muddy, bitter kind of flavor, sometimes with more pronounced acidity, if held warm. If you were to make a straight espresso, it's optimal to drink it within 20-30 seconds. Brewed coffee can usually be held warm around 30 minutes before pronounced deterioration becomes obvious.

A popular Japanese TV show suggested perhaps stirring a pinch of salt in to stale, reheated coffee, which may trick your tastebuds enough into tolerating it. I've found that tactic less than adequate, but your mileage may vary.

There's a ton of information on coffee flavor compounds and other coffee-related research at: http://www.coffeeresearch.org/science/aromamain.htm