Star Trek: 10 Things You Didn't Know About Romulans
1. Model Behaviour

The behind-the-scenes story of the Romulan Bird-of-Prey would no doubt go down well with a glass of the blue stuff on Romulus itself. The studio model, designed and built by legendary prop maker Wah Chang, was used in Balance of Terror and then was never seen again.
As confirmed in Star Trek Compendium (1993), "No additional shots were ever taken of [the Bird-of-Prey] miniature after this episode's effects photography was completed." The Deadly Years used stock footage of the Bird-of-Prey, and after that, as stated on screen in The Enterprise Incident, the Romulans had started to use Klingon ships.
If the in-universe explanation was, as further pointed out in The Making of Star Trek, "due to a recent alliance," out-of-universe the studio had struck a deal with model maker AMT for use of one of their master tooling models of the Klingon (D7) Battle Cruiser as a filming miniature. Most likely, the Romulans had three Klingon ships (or two in the remastered version that included a CGI Bird-of-Prey) in The Enterprise Incident to make the most of what was essentially a freebee and to honour the deal with AMT.
However, they could never have re-used the Romulan Bird-of-Prey in the first place. After filming of Balance of Terror, Chang's model apparently disappeared. Whether it was lost, destroyed, stolen, or made its way to a private collector, nobody really knows. There is one final explanation, apparently given by Chang himself.
Chang, who created numerous other props for The Original Series, never received credit for his work due to endless legal conflicts with the propmakers union. That much is true. Chang himself then reportedly told National Public Radio in a 1982 interview that he became so frustrated with the union issue that he took a sledgehammer to the Bird-of-Prey. None of this can be verified, but failing all else, it would have been the delightfully Romulan thing to do!