One reason the Byzantine Empire outlived the Western Roman Empire was that?

It's the matter of Authorities' strength.

The Western World was blown up from inside, there was no just one great ruler.

Barbarian kingdoms within Western Empire started to rise up against Rome.

Also the role of Bishops of the City of Rome (Popes) increased, when Emperors' position were sloping down.

The Eastern World was internally consolidated due to the Islamic thread. One strong emperor was not merely sign of state power but also, not officially, a head of the Eastern Orthodox Church.