Why does coffee taste awful after reheating it in a microwave oven? I brew my coffee with a percolator using finely ground beans and it comes out great when it is still hot. However, I have to brew at least two cups in the machine. So if I make coffee in the morning, the afternoon cup is cold and I have to reheat it.

If the coffee gets cold and then I reheat it in a cup in the microwave, it tastes terrible! Why?
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