My college Latin professor used to say "Latin isn't dead; its just mispronounced". It was a gradual process of several centuries that Latin evolved into the Romance languages. Really up until the time of Dante, the Romance tongues were considered corrupted Latin. It took Dante to prove that Italian could be a literary language in its own right.
400 years later, we can still read Shakespeare without too much difficulty. I expect it was like this with Latin as well.