Livy, like Plutarch and like pretty much all of the lost works of antiquity, had much of his work lost at the end of the Classical Period and the beginning of the Middle Ages. There are many, many reasons why any given work survived or did not during the Middle Ages, but with Livy it seems that the length and complexity of the work did not lend itself well to the conditions under which works were copied. Many of the texts we have now we're either preserved by the church for religious reasons or perceived philosophical importance, or for use as teaching aids in learning to read and write Latin, as well as to practice copying manuscripts. Livy satisfied none of these conditions, being largely absent of philosophy useful to the church and being much too long to teach or browse through. Despite the fact that many copying bodies, mostly monasteries, vowed to preserve everything they had, paper and time were expensive and copying had to be prioritized. Already by the end of the Classical Period there were also issues with the text, due to the length and certain idiosyncrasies of Livy's style which made copying difficult. Since Livy published his work periodically in decades (packets of ten books each) it was usual for copyists to copy the works not as they were compiled but in the packets in which they were originally published. This meant that by 391, AD, when the consul Symmachus commissioned Tascius Victorianus to review the texts and compile a recension of the first decade, Livy's work was already in a weird place. Our manuscripts containing books outside the first decade (for which we have by far the most manuscripts) and dating from the Middle Ages unfortunately contain some pretty large gaps around book 45 or so due to severe date to the manuscript they were copied from some time in the 5tth Century. Work on Livy's text is one of the hottest areas of research, because friends turn up all the time. A palimpsest with a couple thousand words of Book 91 was found in the Vatican in the late 18th Century, with another long palimpsest, the Verona Palimpsest, contains a sizeable portion of the first decade (even though we have plenty of texts of that), and fragments up to 40 lines are being found in Egypt all the time. Archaeological sites bear hope of finding fragments all the time, with the spectacular hope back when Pompey was uncovered that many of Livy's books would be found there.

Why do we know about Livy's lost books? Well first of all we know quite a lot of lost works by great authors. These works are often referred to by other authors, and there are catalogues and summaries of them all over prepared during the Middle Ages or often before. Livy's a somewhat special case, though. He only has one major work, and it's enormous. Already by late antiquity because of the sheer size of the work it was much more common to refer to summaries of Livy, called epitomes. the epitome of Book One exists intact, and the Oxyrhynchus Epitome, unearthed at Oxyrhynchus in Greece, preserves, greatly damaged though it is, the epitomes of Books 37-40 and 48-55. The remainder of the books' contents (except for two books) are known to us through the Periochae, which were summaries of the epitomes and were compiled probably in the 4th Century.

Plitarch is a different beast. The Catalogue of Lamprias attributes 227 works to Plutarch and we have 78 non-biographical works (some not on the catalogue) and 50 biographies. Much of his work outside the Lives was compiled in the Middle Ages into the Moralia, a collection of moral works. The Lives mainly derive from Roman texts of late antiquity, because the Romans adored the Lives and copied so many texts that we have quite a lot of them left. The Byzantines preserved many of his texts (remember that Greek was not being copied in the west by the church), and luckily Byzantine scholars bad slightly more resources at their disposal, allowing them generally to preserve a little bit more. Plitarch, because of the educational value of his work and his fluid and interesting style, was used extensively as teaching texts, and his work was collected by scholars like Maximus Planudes. Plitarch was also, as we have seen, an even more prolific writer than Livy (which is saying something, since Livy apparently spent pretty much all his time writing) so it's reasonable that more of his work would survive--particularly since Byzantine monks preferred to preserve the works of writers of the Second Sophistic