Rulers of the know world and we don't remember one of the central languages they spoke and wrote in. I know Greek was also somewhat common and there were others. Do we know how the spoken version was forgotten?
The spoken version was never forgotten. Languages change over time. French, Spanish, Portuguese, Italian, and Romanian are all Latin that's evolved, just like English is Old English that's evolved.
Thanks to the strength and regularity of the Roman school system, Latin remained fairly unchanged even into the fifth century. With the fall of the western Empire, however, the schools began to dissolve and Latin began to change into what we call proto-Romance languages. The speakers of this (really these - there were many dialects) proto-Romance would still have considered themselves to be speaking Latin, however.
The thing that actually "killed" Latin, by which we mean it was no longer spoken as a birth-tongue or cradle language, were the Carolingian reforms of ca. 800. These reforms codified "Latin" as the classical or biblical form of the language and defined what people actually spoke as a rustica romana lingua - a rustic Roman tongue. This process happened a bit later, in the mid-10th century in Italy, where the language was closer to classical forms for longer; an Italian speaker could probably understand Latin without formal training until the late 12th century.
Although the division of Latin from proto-Romance killed Latin as a language, it nonetheless persisted in common, spoken form among the learned and the elite. Indeed, Latin persisted as the language of academia into the 19th century, and the ATMs at the Vatican still offer Latin as a language choice.
Unfortunately, the definitive works on this subject are both in French:
Riché, Pierre. Education et culture dans l’Occident barbare, VIe-VIIIe siècle. 4e éd., rev. et corr. Points H195. Paris: Editions du Seuil, 1995.
Norberg, Dag Ludvig. Manuel pratique de latin médiéval. Paris: A. et J. Picard, 1968.
You may want to ask /r/linguistics as well.
It's not dead at all. Besides the Romance languages, 40% of English vocabulary comes from the Latin or Old French (aka Vulgar Latin or Late Latin or Franco Latin). There are countless legal terms, medical terms, common phrases and everyday words we use in English that are without a doubt from the Latin. e.g., ("exempli gratia" from the Latin), per se, vice versa, bona fide, verbatim, status quo, etc. (et cetera is also from the Latin)