I'm sure the answer will be different from different reasons, but was there a period of time when the power of Latin waned drastically? Is there a particular reason French then succeeded Latin as the language of diplomacy?
So, this is a slightly exaggerated claim from MacCulloch, in that - especially in the secular aristocracy - literacy and proficiency in Latin was common but not universal; see, for example, the tendency to illiteracy in the early Norman and Angevin kings. But on a wider scale the point he makes is a good one - that Latin as a shared language of devotion enabled it to work well as a Lingua Franca for much of the medieval world's rulers.
On the same note, a convincing case could be made that Latin lost its pre-eminent position in the 16th century. The emphasis of the Reformation in worship being carried out in the language of the worshipper and its concomitant translation of the bible - while the humanist movement prompted a significant program of translation with regards to classical works - served to diminish the importance of Latin as a language, although it remained a significant aspect of most education (as a read rather than spoken language).