I've learned to an intermediate reading level Latin, Greek, Sanskrit and Classical Arabic. As a foreign language teacher, I'm well aware of current SLA research and the focus on communication and authentic, real-world applications. But these just don't come up, really, with languages that we have only in writing.
Right now, even after several years with these languages, I still have to use a dictionary and think explicitly about grammar when I read a "difficult" author like, say, Tacitus. By comparison, I can read without a dictionary and without explicitly thinking about grammar in Spanish or German, neither of which are my native language.
Which leads me to my question: How fluent is it possible to get (and how can we measure this properly) in reading-only languages like Latin and Greek? Do, and how do, graduate students and informal experts in the languages gain a fluency such that they do not have to use a dictionary very often and do not stop to puzzle out grammar explicitly?