I think the only time a player is restricted to attacking an enemy once per round is if that enemy is engaged with that player. Enemies in any other state (engaged with other players or in the staging area) may be attacked as many times as a player has eligible attackers.
I can completely understand your point of view, I just don't believe it's supported clearly in the rules as written.
Does anyone have the email for rules questions? I think it used to be at the bottom of the page but I can't find it...
Can I attack the same enemy three times in a round?