In 1914 in War and the International Trotsky wrote that the collapse of the Second International was the collapse of the model of a federated international of national workers' parties. In 1918 on May Day he wrote that the significance of May day was it's status as a day of International action for the class, international action which had been derailed by the various national parties of the SI. In 1920 in a report on the upcoming Comintern congress he wrote that the CI was an International party and all the national sections had the right to enquire into the workings of the other national sections and make policy accordingly. In 1938 during the founding of the Fourth International he referred to the International as simply one international party.
Without having seen any evidence to the contrary then, it seems clear that from 1914 to his death in 1940 Trotsky held to the idea of building a single international communist party. Unlike the Italian Left however, who also held to this idea, the Trotskyists by and large seem to have abandoned the idea of an international party. At the very least, they don't emphasise it as much as we do.
I'm wondering why they dropped the idea. Is it simply that the idea of an International party is important in the history of the Communist Left when discussing Bordiga's intervention at the 6th enlarged executive, and so tended to get reinforced. But the idea of the International party is surely also important in the history of Trotskyism, since it was part of Trotsky's analysis of the need to break with the Second International and found a new, Communist International. Is it just that the Trotskyists have never read Trotsky properly?