The easiest form of comedy is cheap cultural catharsis, which is something that shows like South Park and Family Guy, not to mention Saturday Night Live, have leaned heavily on for a long time. You bring a lot of people together, point at something bothersome and say, "look, don't we all recognize this as being worthy of dismissal?", and everyone laughs to signal their approval. I don't think any comedy ages quicker than that - it's like junk food relevance, easier than pointing up something more substantially universal.
To be fair, writing a comedy that's funny forever is nearly impossible, because comedy itself changes so drastically, which is why, as someone else noted, actors essentially become translators. "Taming of the Shrew", on the page, is crushingly unfunny, but in the hands of acting alchemists like Raul Julia and Meryl Streep, it was solid gold.
Woman of the Year's showstopper, "The Grass Is Always Greener", now makes no sense to anyone but people who were alive then and people whose parents kept Erma Bombeck books in the bathroom. Was "That Was A Real Nice Clambake" ever a funny number?