Neither I nor the Orc, however, are committed to remaining in combat until a winner and loser has been decided.
This is not at all clear: AD&D has rules for evasion and extracting oneself from melee; so does 5e D&D.
Why can't the same sort of thing be done in a skill challenge, if it so closely maps to combat?
The stakes of the skill challenge are (I'm assuming)
can the PCs persuade the Baron? The GM is not at liberty just to declare that the players lose, any more than the GM is at liberty, when adjudicating a combat, to just decide that the Orc ducks (because that's what the Orc would
really do), that the Orc runs the PC through with its spear (because that's what would
really happen), etc.
To elaborate: in D&D combat, the GM is not at liberty to decide that
really the Orc would have ducked even though the to hit die shows that the Orc was struck. Rather, the dice tell us whether or not the Orc is able to duck.
In a skill challenge, the GM is not at liberty to decide that the Baron would
really walk away from the PCs who are trying to extract a concession from him, even though the players have not yet failed the skill challenge. Rather, the dice tell us whether or not the Baron has the will and/or inclination to walk away.
Any given person may or may not wish to adjudicate combat in that fashion, or to adjudicate interpersonal interactions in that fashion, but
the way in which they work and
the way in which they generate shared fiction is not mysterious, in either case.
Why can't the Baron just walk out when he realizes things aren't going his way but before he has to suffer the embarrassment of losing; or when he has the upper hand but either doesn't want to embarrass the PCs or decides they're just not worth his time?
Are you asking about the fiction? That's part of what the GM has to do in narrating the skill challenge.
Are you asking about the mechanics? For the reasons I just stated: the GM doesn't have unilateral power to decide that the players lose.