By the same use of high Latin, ie that used by the politico-literary elite, throughout the western empire. In the East of course koine Greek served the same purpose. Romance languages began to diverge concurrently with the political challenges to Rome and the progressive dissolution of the western empire in the 5th century. Sardinian was the earliest in the 3rd century, the period of the military anarchy. So long as Rome is united, high Latin can continue. Literary Arabic is based on the Quran, Latin doesn't have a similar text - Jerome's Vulgate Bible notwithstanding - and so needs political unity as the catalyst for the continued dominance of high Latin. Nationalism, with rare exceptions, is an essentially modern phenomenon based on the nation-state.
Of course Latin was the European lingua franca for the church and scholars right to the 20th century. It was used by the Hungarian parliament as its official language in the 19th century because of the great linguistic diversity of the kingdom of St Stephen. When Primo Levi emerged from Auschwitz, he was able, through his classical education, to communicate in Latin with a Polish priest. It is really only in the last fifty years or so that this cultural primacy has slipped.