I've always found it strange that whenever this battle is mentioned, it's always surrounding death. When Zoro asked Mihawk to train him, Mihawk said he'd be training the guy that wants to take his head, not just beat him. It could just be fancy word choice, but I wonder if it's more. After being trained by him and coming to respect him would Zoro really be the type to kill him?
Mihawk being based off of Dracula/Vlad gives off strange vibes too. Like I don't think Oda went the goth vampire route for nothing but 'cool' points. I wonder if it's one of those cases where Mihawk can't die except in battle, like partial immortality or something to be released. Just an odd theory of mine.