I've often thought of it as not that they don't have warp drive, but that their power source is simply an Impulse plant. The NX was also that type of ship. Everything was tied into the Impulse Engines rather than the Warp Drive. The Warp Drive could produce an immense amount of power, capable of making the ship travel Faster than Light, but they couldn't harness that power (for whatever reason) to power the ship's system. The Federation had solved that problem when they debuted the Constitution Class, but the Romulans hadn't yet done so. The encounter between the Enterprise and the Bird of Prey convinced the Romulans that they needed help, and turned to the Klingons, who had also solved that problem with the D-6 Battlecruiser. Up until that point, the Romulans hadn't realized that the Federation had gotten so far ahead of them technologically.