This may be in the works already, but I think it could be a cool mechanic if there was something like:
He Who Runs Away: If a Mythic creature or party flees from this Mythic creature, a +2 bonus is gained on Initiative and AC on it's next encounter with the mythic creature or party. This represents the experience the Mythic creature has gained on fighting that particular Mythic creature or party.
Could encourage more unexpected recurring enemies in a campaign. I can't think of the exact examples at work, but I'll have to pull out some of my books on mythology where a hero was hunted throughout his journey (lame example I can think of now would be in the original Clash of the Titans where Calibos hunted down the hero.)
Or maybe that's how a non-Mythic creature gains it's Mythic power, by causing a PC or party to run away.
I'm considering this for my ongoing playtest, if the party decides to run away.