So, there's been a little speculation here and there as to why the N-X class wasn't really seen later while other starship classes flourished. While this is usually attributed to difficulties in adding a newer, more powerful warp core. However, I think this is incorrect - the ship was more than capable of having it's warp drive replaced. However, the hull itself simply wasn't capable of it.

First off, we know that it seems the ship is actually able to cruise at it's top warp speed - something that other ships later on aren't able to do (Similitude, Episode 3x10). Tucker modifies the warp drive so that the ship will be able to cruise at warp five - or at least, close enough to it to not matter - and there's never any particular issues with staying at maximum warp, save for later damage that the ship sustains.

So, obviously they can push the ship faster. And it seems that there is some discussion of that, in E² (ENT Season 3, Episode 21) as far as the ship's warp capabilities go:

LORIAN: We got these schematics from Haridan traders. We can use them to modify your injector assembly. You'll be able to travel at warp six point nine for brief intervals.

T'POL: The hull wasn't designed for that speed.

LORIAN: We'll show you how to reinforce structural integrity. You'll be able to reach Degra in less than two days.

This of course wasn't done, as the structural integrity modifications weren't enough to provide an adequate safety margin (there was around a 22% chance of the ship exploding)

ARCHER: You should have told me. My ship could be destroyed.

LORIAN: There's only a twenty two percent chance of an overload.

ARCHER: I'd call that a damn big risk.

So the modifications were never made... or were they? In Seasion 4, Episode 12 we're treated to the following:

ARCHER: Let's see what those new injectors can do

TRAVIS: Five point oh two. Point oh four. Five point oh six.

T'POL: They're falling behind.

TRAVIS: The injector's stabilised. We're holding speed.

Which seems to indicate that they have upgraded their injectors for higher speed and are able to hold the slightly higher warp speed But, referring back to E² - the ship's hull likely isn't capable of much higher speeds without breaking apart. This is further supported by a line in The Augments (4x06):

T'POL: They've detected us. They're accelerating.

ARCHER: Stay with them, Travis.

TUCKER [OC]: Tucker to Bridge. If we go any faster, the nacelles are going to fly off the pylons.

All of this implies to me that the ship's engine is capable of much higher warp speeds - up to 6.9 or 7 - but the hull just isn't capable of the stresses generated much higher than Warp 5. Given the on-screen evidence, I'd say it would probably top out at 5.1 (given that the top speed seen is 5.06 without any structural problems) - but past that it'll fly apart.

This, added on to the fact that the engine can apparently match Vulcan ships, or at least get rather close to them means that there's really no incentive to build more NX class ships versus building something a bit sturdier that can take advantage of the higher speeds. They might build a few more in the mean time... but eventually it'll be replaced by other ship designs that can be faster. Given the small number built and their speed limitations - even with other upgrades they could get (shields, better weapons, better reactors) - it would explain them being phased out of service by the time TOS rolls around, or even the new movie universe, despite TOS era ships being around much, much longer. The NX-class is a successful testbed for the new engine, but ultimately a failed design.