How and why did the eastern half of the Roman Empire not only survive but prosper

The Eastern Roman Empire survived, because they had developed a well organized system of government, a stable administration or civil service, a good army. Most importantly, it was far from the areas which suffered the Germanic invasions which precipitated the falls of the western part of the empire. However, not long afterwards it suffered invasions by Arabs and Slavs which led to the loss its territories in Egypt, Asia, apart from Turkey and part of the Balkan peninsula.