[MrFlibble]

To hold a province, it's wise to build a fortress and place at least a single unit inside (e.g. a peasant militia). That way the enemy hero will have to besiege the fortress before he can finally conquer the province, even if your province guards are too weak to hold the enemy hero in the first place.

That will spare you the endless clash for a province when each side can conquer the province with their heroes but can't hold it with only weak AI guard troops. (I also think that population happiness is negatively affected when a province changes its owner frequently).