Having a 1v1 fight with an animal other than a boar, fair or cheesing, is annoying. Without horses or swords/b12s/str that are high enough in value to one shot the animal after getting the openings up the animal will flee after you do a couple of hits. Now I guess fleeing makes sense however, when the HURT animal runs at a speed that is higher than any speed a player can ever hope to achieve without the help of a horse it becomes annoying.
Solution without making cheesing easier-
If the animal is doing damage to the hearthling at all the animal will not flee.
You could also make the AI realize that its not able to use combat moves constantly and is not on cooldown it will flee or lose interest.