I have heard two different versions of why the original Romulan ship never appeared again:
1) it got broken, and the budget wouldn't allow for repair.
2) Gene hated it, thought it looked bad on screen, and would not allow its use again (possibly had it destroyed).
It's all speculation: take your pick.
The Romulan vessel model was only ever used in "Balance of Terror." Any subsequent episodes where it was featured was just stock footage from BoT.
Which episodes were those?
AFAIK, the Romulans only appeared in Balance of Terror and Enterprise Incident. TOS-R decided to make one of the ships in the latter into the ship from BoT, but in the Original Series I believe that ship appeared only in that episode.