Even though Claudius' history was written in Greek, the Byzantines might not have been interested in the Etruscans. Maybe they scraped the parchment for other use, and we'll find it underneath something else.
Claudius introduced a couple of letters to the Latin alphabet which didn’t survive him; he spent more than half his life (prior to his elevation) in study, spoke multiple languages, read and wrote in them, and his history of Etruscans vanished. It’s easy to understand how stuff from that time hasn’t survived, but so little of his work survived, perhaps he was really just a dilettante, or perceived as such. :’) OTOH, after he became emperor, it became a little dicey to quote his work during his lifetime, and probably a good idea to consult with him to make sure it was okay. That too could account for its nearly total loss.
http://en.wikipedia.org/wiki/Claudius#Views_of_ancient_historians