I might be able to understand the unwillingness of the AI to admit defeat in the face of overwhelming odds, it happens, people would rather die than submit to another. But this is just ridiculous...

New Byz campaign. I take the Turkish capital Iconium and the Sultan falls. 2 Turns later, march to within 1 square of Caesarea, their new capital. Its defended by 2 peasant archers and the new Sultan. I have small army (General, 2 spears, 2 Trbz and 2 Arm. archers, 1 HA). So now an at-war army is sitting 1 square outside their capital and only remaining family member - they should build more units and prepare for a siege right? They even have a 4 unit army (can't see what it is) within marching distance. They have the money and armies within reach to defend with 8-9 units, but instead they build no units and move their archers out of the city and let me massacre them while their lone Sultan comes in as reinforcement from the castle. Needless to say he was killed and the Turkish empire collapsed. Now it is just me and the Egyptians and a dozen rebel provinces.