I think Arthur is heroic not only because he is brave and courageous but also because he strives to live up to the code of honor he sets for his knights. He really tries to follow his code even when it is not of benefit to him. For example, he give Mordred a place at court because his code of honor requires him to do so even when he know that Mordred is dangerous. He does not want to acknowledge Launcelot and Guenever because it would break the code by bringing a lady to dishonor and would not be in the best interest of the kingdom. Even after he is at war with Launcelot, he is willing to meet with him honorably. Finally in the end it is not really Launcelot and Guenever that bring about his downfall, but it is the son he know he should
