Apologies if this has been asked and answered, earlier.

Last campaign game, Gaarkhan was getting whupped on. One attack did enough damage to trigger his Rage ability, so he became focused. Another attack, from a different enemy entirely, put enough of a shellacking on him to drop him to Wounded. The question then arose, upon becoming Wounded, does Gaarkhan lose his Focused status?

in the spirit of keeping things moving, I allowed him to keep the status, as I was unsure as to exactly what would happen to it. But it does raise the question: When a Hero becomes wounded, do they lose any conditions, either harmful or beneficial?

Becoming wounded does nothing to conditions. You flip the hero sheet over, remove damage tokens, and remove excess strain tokens.

Note that if Gaarkhan isn't focused already when he becomes wounded, he no longer has Rage, and cannot get focused from that attack even if he suffered enough damage from it.