Designs can be around for a while merely upgraded with current materials, design elements and technology; individual ship's less so. Take the Miranda- or Excelsior-Classes, they've been in operation for a century (by the last canonial time we see them) but there's no evidence to suggest that the U.S.S. Miranda
or U.S.S. Excelsior
are still in active service. For all we know, most of the ship's that we saw on screen had only been built in the last twenty years.
There could be NX-Class ships still buzzing around in the 2260s, 80s or even the 2300s, but they wouldn't be from the original production line (they might not even be Starfleet, but used by civilian agencies or private individuals). Seeing how the Klingons are a pretty stagnant race, I doubt they would alter designs that much over time.