The Eastern Roman Empire centred on Istanbul, survived for 1000 years, after the destruction of the original Roman Empire based on Rome. Istanbul was the richest and largest City in the Mediterranean. For many years, it thrived in-spite of being the target for all its neighbours. For most of this period, it was on the defensive.
Its enemies had very different approaches
The Franks – full frontal charge of heavy armoured cavalry
The Turks – highly mobile mounted archers
The military approach could best be summed up – “we live another day”. Therefore they used the most effective approach to repulse their enemy. This was a complete contrast to the Chivalry code vaunted by the Franks, and western European knights. The false retreat, hit and run tactics, bribery and treachery were all used, ideally to stop fighting a battle, or if a battle was inevitable, then ensuring the best chance of victory.
With the siege of Nicacea in 1097, the Byzantines supported the 1st Crusaders during the siege, but the night before the Final assault, they agreed to spare the Defenders and entered the City, across a lake. The Crusaders, the next day found the City held by the Byzantines and went on their way empty-handed. The Byzantines had gained a very well defended city for minor losses, (unlike the Crusaders)
With the Turk raids, the local militia would try to slow down the raiders and restrict their option. Once the raiders were heading home, they would be harried to leave behind the booty, but not trying to trap the raiders. The intention was reducing the reward from the raid, increasing the cost with injuries and losses (rear-guard actions are difficult to manage) but keeping their own losses to a minimum.
The Byzantines were effective for 1000 years by being flexible and innovative. However there were other aspects that were not so commendable like politics and murders.