Hello Smich88,
What Prezs has explained is correct, if the morale drops below 50 during the simulation of the battle, it would be safer to not send the fortress siege because there is a chance (progressively increasing by 2% with every Morale point below 50) for your army to flee. But you can't predict when exactly is this going to happen, sometimes the army may continue fighting with lower morale values. Attacking army in a fortress siege is deployed in three lines, front line where all melee units and Battering rams are deployed, second line with Archers only and third line with all siege engines. Each line has its own morale which changes according to the inflicted damages. For more information, please read Fortress siege and Global morale -
http://www95.imperiaonline.org/imperia/game_v6/game/help/?section=military&lang=en&speed=2#military_56.
Swordsmen and battering rams from the first line, sent by the attacker in the battle above, were attacking the fortress walls, their morale dropped to 44 in round 10 but they managed to destroy the fortress and they didn't flee. The units from the first line continued fighting in the next 2 rounds against your garrison army and they managed to destroy it before they fled due to a low morale. PEPELUIS79's archers remained on the battle field and he won the battle.