I've never noticed the AI getting fatigued before. How do you know they are fatigued? Is it just your assumption?

Personally I see the opposite problem occurring. The AI just doesn't hurry fast enough, especially when it's sending reinforcements. I've lost count of the number of AI cities I end up taking uncontested because a reinforcing AI army comes to the city's "rescue" and the defenders then sally forth. Because either the reinforcements or the sallying army or both advance toward you so slowly, it's really easy to destroy one army and then the other in turn, leaving the city undefended. I see this as quite a major problem for the AI, it makes taking cities absurdly easy.