Makes sense; could the CSA winning (PoD in 1862) do the trick?
Certainly! This would almost require magic, after all, and wizards' duels are a staple of fantasy literature.
More seriously, to make dueling continue to be accepted in Western society, we would need to make broader Western society resemble that of the countries where dueling held on the longest. This would be South America, specifically countries like Uruguay (which only outlawed it in 1992) and Peru (where it has not been outlawed and is still even semi-accepted, though AFAIK none have been publically waged in some time).
It's been supposed (ex.
here) that the vast majority of duels waged in South America were between disputing politicians of opposing parties or between politicians and press figures. By fighting a duel, a political figure generally hoped to both build a name for themselves and to force the other party to accept them as honorable & worthy of respect; if you fought a duel, you were above the rabble and above suspicion, and your authority was thus legitimized.
I think that if you were to create such an environment in either the US or UK - where dueling was the most frowned upon, and thus where a cultural reversal would have the most effect - for an extended period of time you could keep dueling accepted until modern times. It would seem easier to do this in the US, because as mentioned dueling was generally accepted in the South pre-ACW. No civil war or a trivial one (Union wins the first few battles and no Emancipation Proclamation is considered) would probably keep the Southern social systems in place a while longer.
I'm wondering, though, if a much longer civil war and harsher peace might actually be the way to go here; if the South is ruled more dictatorially from Washington, and overt resistance like the KKK more violently stamped out, former Confederates might cling to dueling as a means of perpetuating a separate identity, as a means of righting perceived injustices outside of a courtroom (which would be of questionable legitimacy), and as a way of striking back against the occupying Yankees. I would think that in this scenario you'd have more people that were actively interested in maintaining the institution of dueling in the face of opposition, and thus better chances of dueling surviving in significant parts of the West until the modern day.