Search for the most iconic chair designs in the world and you'll likely come across a list that includes:
Wassily Chair by Marcel Breuer (1928)
Barcelona Chair by Mies van der Rohe (1929)
Grand Consort by Charlotte Perriand, Le Corbusier, and Pierre Jeanneret (1928)
The various Eames Chairs (starting in 1945)
Wishbone Chair by Hans Wegner (1949)
Wiggles Side Chair by Frank Gehry (1972)
And the list goes on.
Most of these chairs also look as if they were just designed yesterday. Meaning, they're timeless and have stood the test of time. But they are mostly older designs. Which raises an interesting question: How much does the passage of time play in a role in determining whether or not something is "iconic"?
There are some more recent designs that you could call iconic. The Roly-Poly Chair by Faye Toogood (2014) and the Louis Ghost Chair by Philippe Stark (2002) come to mind. This suggests that really great designs can become immediate classics. (Though, this latter example is a reinterpretation of a classic French chair that in and of itself is an icon.)
What I think is the mostly right answer is that, yeah, sometimes you can catch lighting in a bottle. The Louis Ghost Chair, for instance, is one of the top selling chairs of the 21st century. It's a clever and modern take that used new technologies (as is often the case) to revisit an old classic. Starck nailed it.
But more often than not, you probably need time. Time is what allows the object to form cultural associations in our mind and to prove that it is, in fact, timeless. However, if this is truly the case, then it makes it difficult to determine if we're still producing as many design icons today as we did in the past. We won't really know until they become old.
Image: Louis Ghost Chair via Knoll