Artifact lost with retreating hero?

If an enemy hero retreats from battle, he will immediately reappear for rehire in their taverns and will not be available to you for the remainder of the week. If the enemy cannot or does not rehire the hero, he returns to the normal hero pool at the beginning of the next week and may appear in your tavern, too.

If the player this hero belonged to can recruit heroes (depends on the scenario, but basically, if the AI-player has the gold and a town where he can recruit heroes in), they will nearly always be rehired by them and you can fight him again to get his artifacts.

A completely defeated hero can appear in the tavern again, but, in my experience, not in the same week he was defeated in. In that case, exercise some patience and let time pass, eventually you can get the required hero unless he gets recruited by another player.