Tips for catching fleets that run away from you:
If you make liberal use of the pause button (spacebar) and hover your cursor over them, you can see what their target is when they aren't fleeing from you. Often they will be "attacking orbital station" or somesuch, so you know they'll be going for the station when you aren't too close to them.
If you click the space next to them instead of clicking ON the fleet, travel diagonally instead of straight towards them, and sometimes outright head in the opposite direction as them, they will often veer back and quickly head towards their regular objective. This is a good time to (again without clicking on them) head back towards them, and often you can touch them just before they turn away, and THEN click on them, causing an engagement.
It can often be helpful to position your enemy between you and one or more groups of your allied fleets, giving them more obstacles to avoid and increasing your chances of catching them as they fumble around and try to change directions.
If you chase a fleet to the very edge of the map, they can't go any farther and you can corner them. This works especially well in the actual corners of the galaxy map.
I've used these methods to catch single-frigate-fleets while I'm a dozen onslaughts strong and my max speed is like 102, so it isn't impossible; It is just tedious.