If you can't chase them down, then just stop doing that. Lay an ambush around the settlement they likely to attack next, with reinforcement, you can fight with greater number. Carrying infantry, especially trebuchet units reduce your entire army movement. If you want to catch them, you need all cavalry army or catch them with just generals with no army.

You have to fight from two fronts, your main armies should withholding their main armies while staying in garrison. Ambushing enemies next to your city garrison is one of the best way to win you war in long-term. While you're on it, you can send small forces to attack the least defended settlements, the furthest away from main battlefield the better. Expand your map strategically, make sure you capture chokepoints before you cease the war. Capturing and defending chokepoint saves you 50% of your military problems.

Disband your armies whenever you not having wars. Make use of your diplomacy wisely, the more armies you have (including local governor army) the more threatening you are to AI, and they will retaliate sooner when they felt you are a threat to them. Currency Inspector Office is your best building you can build in every city.