The duration of panic depends on the circumstances of the panic. The morale of your/enemy forces is dependent upon the relative battle rating of the armies. If you have a vastly superior battle rating, then your morale will rise, and the enemy's will fall per turn, and vice versa. However, if you use a spell to panic the enemy, and if they have a superior battle rating, their morale will start to rise slowly, while yours still continues to drop. Once an enemy is in a state of panic, they will not move or attack on the turn *AFTER* they get the panic status. You have to think of your tactical turn, and the opposing force's tactical turn as one actual turn. So that is why you have to wait till after the turn that they've been hit with panic for it to take effect.
The spells that cause panic are also among the most broken in the game right now imo. As if you come up against impossibly hard encounters, you just panic them and that is that. You can take your time beating on them with almost no resistance. Unless you forget to keep them demoralized, at which point they awake from their stupor and own your face.