Not sure what source you are using -- NT Greek ceased to be the language of the Liturgy for the West at the end of the 2nd century, and became Latin. Latin was the "popular" language, since it was spoken by Latins (geez!), but the liturgical Latin was way above your average Roman, as any liturgical language is not the same as "vernacular," i.e. spoken language.
After that as far as I know -- until the Vatical II - (liturgical) Latin remained the language of the Latin Church universally for all liturgical and ecclesiological rituals.
RE: Changes in liturgical language in the West
Indeed the change from clerical Greek to popular Latin did cause a brief schism in the See of Rome in the early 3rd century. Clerics, most of whome were Greek argued for the universality and sanctity of Greek as most of the Christian world understood the Greek of the NT. Populists and native Roman clerics prevailed because, they argued, of the importance of having worship in a language (namely, Latin) that the people understood.
An interesting side note: the brief anti-Pope Hippolytus, who represented the conservative Greek faction in the Roman See in the early 3rd century is also the author of the work entitled The Apostolic Tradition concerning the regulation of ecclesiastical life. He probably wrote the work in 215 AD just prior to the schism as a justification of the Hellenic tradition in Rome. The division that followed and the fact that Hippolytus wrote The Apostolic Tradition explains why the work was almost entirely forgotten in Rome and the West while in the East, in Egypt and Syria precisely because it claimed to present the apostolic tradition from Rome it had a tremendous success. It would be a mistake to envision this text as THE Roman Mass of the 3rd century, pure and simple. At this time there was still no fixed formulary for the Liturgy, but only a fixed framework which the celebrant fills with his own words, as older texts clearly indicate. Rather, Hippolytus presents his text only as a suggestion, and expressly stresses the right to freely extemporize a text as a right which remained long in force. The right that Hippolytus laid claim to in his famous work. Hippolytus would later reconcile with Rome and died a martyr for the faith.
When Rome fell, the facility of Latin left the people, who began to develop native languages (the so-called Romance languages) of their own. This process was certainly under way by the 6th century. Latin then became a language preserved almost entirely by clerics. By the time of the Middle Ages, the Latin used by the clergy had developed into its own dialect (so-called Ecclesiastical Latin) and Europe developed its own popular languages.
adapted from: The Mass of the Roman Rite its origins and development, JA Jungmann.