Latin has never died out, it has been transformed over time and morphed into different modern day languages while religious practice has kept something close to the original form alive and spoken as well.

Modern day languages are grouped in families of language groups with common roots, among which we have the Indo-European Language family - all language groups counted towards this group are originally spoken in cultures located in Europe and Asia. This large umbrella term includes literally dozens of languages sorted by their geographic and ethnographic origin. Among these you can find a branch of languages that all have vulgar latin, or what is generally understood as the commonly spoken form of ancient latin, as their common root-language. This branch includes all areas that have been conquered and controlled by romans for a very long time and have, later, mostly remained under christian influence. Thus, the latin influence has never left their language entirely.

This means, all of these languages come from a combination of whatever language has been spoken at their geographical area before the roman conquest, the latin dominant influence during the occupation, and the continous cultural influence after the Romans left. The Romans pretty much implanted roman influence into whatever cultures and languages could be found in the areas they conquered. With latin as language of government and written communication, and vulgar latin as spoke language of the soldiers and traders, people needed to learn the language and adapt for terms they didn`t have in their old dialects. Often, the Romans remained for such a long time that much of a culture`s old language was overtaken by vulgar latin, too. We call this particular language family Neo-Latin Language group, and you can find Spanish, Portuguese, French, Romanian, Catalan, and Italian in this group. There are other languages, outside of this group, which have latin words in common with these Neo-Latin languages, such as English, or German, but their development is a little bit more complicated and will be not included at this point.

At any rate, the Neo-Latin Languages have different amounts of closeness to vulgar latin, and thus, not all of them carry the same amounts of old words as the next one, but they all use a substancial amount of word-roots you can find in ancient latin even in their modern day commonly spoken dialects. While italian is viewed as the modern day language the closest to vulgar latin, which is certainly owed to the fact that it sits at the location of the ancient center or the roman empire, and has been heavily influenced by religious tradition, too, French has become the language the farthest away from its latin roots. You can, however, see some of the complicated roots of latin grammar rules in modern day french grammar, too, so it`s not impossible to find the similarities if you look for them.

Furthermore, the amazing thing about latin in particular is that something very close to the original root language has still survived in a written language form. Although modern day latin is not exactly the same as ancient latin, or vulgar latin, you can still follow it`s own development over the centuries by studying what religious tradition has kept alive. It would go entirely too far to go into detail on this part of language history here, but I need to include that religion has aided, at least during the later centuries, to keep latin roots alive and renewed influences into the language where they might have otherwise died out over time. Thus, religion has certainly played its part to keep latin alive in written and in spoken form.

So, as you see, latin has never been lost entirely. It has morphed into a whole group of modern day languages, and religious tradition has kept at least some form of the original alive pretty much for the entire time. We think it has died out nowadays because no country still speaks what we assume is the original true form of latin anymore, but while the language might not be preserved in its true form, there a billions of people speaking modern day latin languages every day, so it really is anything but dead.