I know this is a broad topic, and it will vary from language to language, but with written texts from places like Rome, or middle kingdom Egypt, or ancient china, are we simply doing our best to decipher things? Or are we at a point where we have a good understanding of the workings of the language. Would you be able to write a letter in those languages to a contemporary of the time?
In addition do texts from the time of say, Constantine the first become easier to understand than those of Cincinnatus?
As you noted, it depends upon the language.
Consider Chinese, where the characters really haven't changed a lot over the past few centuries. Of course, if you go back thousands of years, the script becomes radically different, but it requires very little training to be able to understand, say, Qing dynasty texts. (The older the document, the more training is required to understand it)
Modern Chinese can be understood perfectly. Literature from the Qing dynasty reveals that the usage of some characters have changed, but there's enough literature written during this time period to study the nuances of characters and their connotations.
Because we can study the language and its gradual progression over time, we can trace characters back to their ancient equivalents, thus giving us a high degree of confidence that we understand what we're reading.
Even if you want to study very old forms of the Chinese language, you can find enough literature that lets you trace the language back through time.
But not all languages have this nice continuum.
Take Hebrew as an example. We have ancient Hebrew, then there's a stretch of several centuries where it's really hard to find many writings (mostly because the language fell out of favor among Jews living in diaspora). So, it's nearly impossible to find a continuum of literature that allows us to trace the language back to its ancient form.
Now, even for a language as poorly understood as Hebrew, we can still understand enough that very few scholars argue about the basic underlying premise of a passage. If you've ever studied a foreign language, you know that you don't need to understand every single word to grasp the gist of what's being said.
If I say, "I took the __________ bread to the market," you understand what I did perfectly. But what type of bread did I take to the market? Or, did I use an explicative? What tone of voice is being used?
Our understanding of nuances have been lost in Hebrew literature.
We know what the author said. But there may have been deeper meanings such as plays on words, rhetoric, and connotations of certain words that have been lost.
So, the answer to your question is "it depends."