The rules aren't very clear on this, I think the best interpretation is that a challenge lasts until the end of the round, even if one of the combatants is dead. This is implied in the "to the death" section where it says that, if the combatants are still alive, and the combat is still happening, the challenge continues as well. This implies that challenges last entire rounds, and could last multiple rounds. But it's not perfectly clear. Seems like this is the intent of the rules, and how it has worked in past editions.
It would create some weird incentives if you could be attacked during a round where you were in a challenge. In your example, it would behoove the general to not kill the champion so that the entire unit couldn't stab him at lower initiative. It would make you try to bring your opponent down to one wound but stop short of killing them, which seems like an unintended result.