Languages are communication systems.
There cannot be anything intrinsically dead about a communication system. Hence, the question whether Latin is dead or living is simply a question of how people treat it. In the past several centuries, millions of people have learned Latin and used it effectively to write and speak with one another, in spite of the fact that none has been able to claim it as his native tongue. In universities today, Latin studies are competing with other disciplines for students, funding and public respect, and have consistently been losing ground to languages perceived as more 'relevant' to the needs of a society driven by the spoken word. The cultural inheritance we have received from the Classical world the Middle Ages and the Renaissance, conveyed to us in the Latin language, is rapidly being eroded away.