Upvote:1
As no better answers (like one which has some information on the census records specifically) have been posted, I'll turn my comment into an answer:
The odds are very strong that those records, like most Roman documents, were written on papyrus and rotted away or were burned in ancient times.
Most Roman records were written on papyrus, as it was cheap (imported from Egypt) and vellum or parchment cost substantially more. (The Wikipedia page for papyrus suggests that costs may have been comparable, but that seems at odds with both other sources and the rather complicated process of making vellum from animal skin.) Certainly we have few original documents from Classical times, and some at least would be expected if many had been written on vellum.
In a moist climate like Rome's (or Alexandria's, be it noted) papyrus has a half a half-life of a century or less, being destroyed by mold and insects even if they were not destroyed by fire or war. An ancient library of papyrus scrolls would have been a firetrap, being comprised of (a) large amounts of (b) flammable materials which is (c) rolled so that air can easily get to the flames. (May I impose on you here to complain about Peter Jackson having Gandalf searching the Minas Tirith library piled high with documents having a big open flame?) The Wikipedia page, for example, notes that papyrus documents more than 200 years old were considered remarkable.
To survive to modern times, papyrus documents need have been recopied every century or so or stored under desert conditions to survive. Putting them in a library did not preserve them unless they were regularly recopied -- an expensive process! Consequently, just about all the surviving Classical papyri were found in the Egyptian deserts.
It seems unlikely that Imperial Rome would spend the money needed to recopy centuries-old census records every hundred years or so and the subsequent Ostrogothic kingdom was even less likely. Note also that the ancient center of Rome -- which is where records were kept -- was subject to regular flooding and was abandoned by the end of antiquity and covered with silt.
Carolingian monks saved a lot of what survived to the 800s by copying it to more durable vellum and parchment, but again it seems unlikely they would have touched the census records even if they found copies of them.
The census records most likely rotted away even before the Western Empire did.