The Gallo-Roman bishop Sidonius Apollinaris (d. c. 480) writes to his friend Didonius in the early 460s describing a villa he visited. Among its other amenities he describes its library:

[I]n yet another [place] were books in abundance ready to your hand; you might have imagined yourself among the shelves of some grammarian, or the tiers of the Athenaeum, or a bookseller’s towering cases. They were so arranged that the devotional works were near the ladies’ seats; where the master sat were those authors ennobled by the great style of Roman eloquence. The arrangement had this defect, that it separated certain books by certain authors in style as near to each other as in matter they are far apart. Thus Augustine writes like Varro, and Horace like Prudentius; but you had to consult them on different sides of the room. Turranius Rufinus’ interpretation of Adamantius Origenes [Origen] was eagerly examined by the readers of theology among us; according to our several points of view, we had different reasons to give for the censure of this Father [of the Church] by certain of the clergy as too caustic a controversialist and best avoided by the prudent; but the translation is so literal and yet renders the spirit of the work so well, that neither Apuleius’ version of Plato’s Phaedo, nor Cicero’s of the Ctesiphon of Demosthenes is more admirably adapted to the use and rule of our Latin tongue. [This is from O. M. Dalton’s 1915 translation of the letters.]

By 500, monasteries were definitely becoming centers of literacy. Benedict’s Rule (c. 520) requires a book for every resident monk to be read during Lent. One historian (sorry, I don’t have his name handy) calculated that the Rule required about 1,500 hours of reading annually from each monk, which required the collection of books to accommodate that need. Until he was put to death in 480, [Boethius’] (http://en.wikipedia.org/wiki/Boethius) lifelong project had been to translate Greek works (like Aristotle) into Latin to preserve the Greek legacy for the Western Empire, where knowledge of Greek was disappearing. Likewise, [Cassiodorus] (http://en.wikipedia.org/wiki/Cassiodorus) (d. c. 585) sought to preserve classical learning at his monastery at Vivarium. He composed his Institutiones as a sort of handbook to classical knowledge that could be used to help interpret the Bible.

In any case, the decline of literacy is well attested for the later Empire, suggesting that educational institutions were disappearing or moving into monasteries.

As for texts now lost, these are too many to count. Off the top of my head I would mention Sappho’s 10 volumes of poems for the most part, which the Romans knew, Cicero’s Republic, most of Livy, lots of Suetonius, etc. We’ve lost even more Greek works, especially pre-Socratic philosophers like Epicurus and the many plays of Aristophanes, Euripides, Aeschylus. Aristotle’s missing treatise on comedy from the Poetics is lost (a plot point in Umberto Eco’s Name of the Rose). There’s a nice list of lost Greek and Latin works [here] (http://en.wikipedia.org/wiki/Lost_work#Specific_works).

It’s worth noting that the overwhelming majority of Latin works that survive were preserved in the monasteries of the Carolingian empire in the 8th and 9th centuries.

Edit: Misspelled Apollinaris.