What factors allowed the Eastern Roman Empire to survive into the early Middle Ages?

After the final partition of the Roman Empire in 395 into the Eastern Roman Empire (Byzantium in the future), it received economically developed and rich territories of the East, where trade, science and art flourished.
The only possessions on the European continent were the Balkans, the rest of the empire was beyond the straits, in Asia Minor, Syria, Palestine and Egypt. Hordes of barbarians passed through the Balkans and settled in the territory of the weaker West, without encountering any obstacles in their movement.