Unlike most other genres, whatever the medium, comedies thought to be good from the past tend to fall flat today. Aristotle thought that one function of humor and comedy is to look down upon someone -- not just as in making someone the butt of a joke, but even looking down on yourself when you realize what a ridiculous situation you're in. Others building on that point to the status-seeking function of comedy. I don't see that so much because that assumes it's an individual satirist taking on his enemies. In reality, it looks more like a way for members of a single tribe to heighten the in-group vs. out-group distinction -- white people dance like this, and black people dance like this.
After awhile, the satirizing group may no longer be influential or even exist, and the same goes for their opponent tribes. A contemporary audience cannot sympathize with jokes about a group who they don't even know about; the group would need to be updated. And most of the comedy tends not to be a blatant attack on the group but a series of more subtle barbs at the group's mannerisms, slang, clothing style, minor foibles, and so on. No one in 100 years is going to know that such things were being spoofed by the makers of Ron Burgundy from Anchorman or the goth kid from South Park. Hell, look at how quickly Napoleon Dynamite vanished from public awareness. Superbad is just about there too.
Certainly every bit of topical humor added lowers the shelf-life of a comedy. It's only one generation later, and yet how many would laugh at a current events or pop culture-related gag from 1985 -- even among those who would still recognize its origin and logic?
On this basis, what comedy previously thought to be funny do I think will be most doomed to obscurity after its initial run? -- Family Guy. Most of the jokes are references to contemporary (or past!) pop culture and current events. What remains is mostly an attack on the tribes that rival with the creators' tribe for social and cultural influence. And even the jokes that don't seem to be aimed at anyone in particular still serve only as tribal membership badges for the creators and viewers -- we belong to the tribe that, for whatever reason, makes these kinds of pointless remarks. We're just weird like that.
I would add all of those dopey series on Cartoon Network like Aqua Teen Hunger Force and Robot Chicken, but I don't think most people found them funny to begin with. Their existence has only been due to their use as a membership badge for a sub-culture of adolescent male dorks. The recent "frat pack" movies starring Will Ferrell, Ben Stiller, bla bla bla will do terribly too, but at least they had to appeal to a broader audience than Family Guy did, so they aren't so pointless.
And which will hold up the best? Obviously those that focus on more timeless and universal themes, not dated provincial turf wars. Those themes are usually the forte of action or drama specialists, though. So drama-comedies like The Simpsons and action-comedies like Ghostbusters will endure the longest. Unfortunately the increase in identity politics and tribalism within American society means that most of the comedies from the past two decades are disposable, with a few exceptions. Still, the action-comedy reached its peak just before then, and it's currently OK to re-visit and enjoy stuff from the '80s. So you won't feel like such a weirdo for going outside the contemporary mainstream.