So far I've been sneaky and avoided saying much about The Hunger Games, especially the way it's been compared (unfairly, if you ask me) to Battle Royale. Without having read Games yet — it's on the agenda, though — I'll just say they seem like parallel implementations of some of the same concepts.
I bring that back up here, though, as a way to talk about a larger subject that the two invoke together: Are the best dystopias just a reflection of the excesses of the time that they were written in, or do they look at something deeper?
This question comes out of some previous musing I've done in the same basic vein: that any work of SF, like any work of fiction, is a product of its moment in time. We can write stylistic imitations of the work of past eras (The Sot-Weed Factor, and a good smattering of recent steampunk come to mind), but what we can't do is write something as if it were a true product of that era. We could, but at the same time we'd know it wasn't a completely honest endeavor. You can't writ, say, Chaucerian-era fiction today simply because the whole of the Chaucerian mindset no longer exists. The best of it (one would hope) has become one with the modern mindset. (Again, you can write fiction set in those periods, but you are not going to have much choice except to approach it with some grain of modern sensibility.)
Likewise, any dystopia is going to be written from a sense of what the wretched excess of the day is. Yesterday's wretched excess may seem like today's quaint and distant concern. Few people expect the whole of the future to resemble 1984 or Brave New World (or We, or Kallocain), but we do fear that elements of those things will have dominion over our lives. In fact, I'd say we're discovering that one of the hallmarks of a dystopia is that the whole vision doesn't have to be accepted in toto for it to be valid. The worst aspects of all four of those books' visions continue to come true every day; they just had the nerve to push their central conceit to become the size of a world.
A good dystopia rarely ages badly, in part because there isn't a single age in which mankind could not be said to be in crisis. There's always going to be something resonant about seeing some aspect of our crises writ large and made into the size of a whole world. We still read 1984 not because we continue to worry about the threat of Soviet Communism but because we remain unnerved by the way those in power are ostensibly determined to continue to stay in power at any cost and by any means — for no other reason than to stay in power. That dilemma is ageless. We, likewise, has its whole meaning summed up in the lines "What is the last revolution?" — words that had great resonance in 1921 Russia, but have lost none of their weight with time and in fact only gained it.
How Hunger Games and Battle Royale (the latter of which I reviewed a while back) hold up and remain relevant in the decades to come is nothing I can predict. Royale has had a little more than a decade under its own belt; its venom is still fresh. Hunger Games only just recently appeared, and so it's even more untested. The only way to tell what in either one will outlast the moment is to wait.