I know Reddit likes to fetishize the LoA as some great vault of otherwise-unknown knowledge, but the basic fact is that for works which were considered "important", they did.

The problem is that no one cared to copy them afterwards, or that they were lost anyway. Papyrus, the preferred medium for Roman writing, is not the most durable thing, particularly when compared to parchment, and is particularly bad at surviving outside of the dry desert conditions of Northern Africa (which is where we find most of our Roman papyri).

When a work was sufficiently degraded, or someone else wanted their own copy, it was laboriously copied over, a process which was quite expensive and took a long time. The labor required to copy works meant that there was an inherent bias towards the types of texts people wanted to read, and the people who could read after the 6th century were, on the whole, part of the Church. This is not to say they only copied the Gospels - there was significant interest in the great literary works of antiquity - but many of the minor authors and more technical (or heretical!) treatises slipped through the cracks. Added to this is the simple fact that monasteries and churches tended to be raided less and thus have their works preserved more frequently, which has significantly biased our preservation of sources.

There was actually an amazing book published recently on source preservation in the Latin west:

• Brown, Warren, Marios Costambeys, Matthew Innes, and Adam J. Kosto, eds. Documentary Culture and the Laity in the Early Middle Ages. Cambridge: Cambridge University Press, 2013.