Jeanne yes, medieval Latin carried on being used - to a point. I wouldn't say it's in heavy circulation nowadays though 
It won't die. It just changes. There was a programme on Radio 4 recently (Word of Mouth?) talking about the evolution of language. e.g. the demise of 'shall' and the arrival of 'the footballer's present tense' (look it up). You can't stop it, nor should you try to.
Languages absolutely can die through evolution. History is littered with dead languages, once spoken by whole cultures, that fragmented into a slew of local variations and eventually just became several distinct languages. If in, say, 400 years' time English as a single language is no longer spoken but has been replaced by Onglish, Inglish Chinglish, Spanglish and Franglais, none of whose speakers can easily understand one another, in what sense is that not the 'death' of English?
I think it's easy to take refuge in relativism about how it's evolution and we can't help it, and so avoid making qualitative judgements about the evolution of language. Yes, language evolves. No, there is nothing a single individual can do about it. But does that mean one can't or shouldn't have a view about the desirability of that change?