Answer:
The eastern Roman empire was known as Byzantine empire. It lasted for twice as long as the western roman empire did. The Roman Empire was divided by Constantine One in 330 and Constantinople was made the seat of power for Eastern Roman empire and lasted for 1100 years.
There were various factors why it lasted for so long, some of the reasons are: Location of Constantinople, The Varangian Guard, Weaponry, Diplomacy, Leadership and religion, Well manged internal affairs.
Constantinople stood on a rocky peninsula and it was extremely difficult to attack and capture it from the sea and if the enemy attacked it from other side the city dwellers could receive supply from the sea.
The Byzantine emperors were very apt at diplomacy although its army never exceeded 140,000 soldiers it still managed to expand its territories and keep it enemies at bay. It was possible due to their diplomatic abilities. Marriage alliances was one such tool.
Due to these reasons it was able to thrive as a capital for more than thousand years.