It wasn't gone in a generation. It took hundreds of years.

Dueling was being mocked in the 18th Century. It transformed into a not-very deadly social stunt in the 19th Century. It did not die out until the years following the 1st World War, give or take a few stunt duels thereafter. Read the account of Aldo Nadi's duel in the 1920s to see what the younger generation thought of it long after it was being mocked. The younger generation has always been quick to "go out back" and sort things out with violence, no matter how much you laugh and call them idiots for it. The only question is why did they stop using swords? (It's questionable whether they ever stopped using guns.)

There were two major sociological milestones in the decline of the duel. The first was the French revolution, which lead to (1) the assertion of upper-class privileges by the bourgeois, (2) a loss of the warrior ethic among the social elites who were no longer chevaliers or knights, and (3) a subsequent decline in the wearing of swords. The first led to the middle classes taking up the duel, but feeling that killing the opponent was in poor taste. Duels became substantially less deadly during the 19th Century, to the point where quite minor wounds were accepted as honourable and even ideal outcomes, since they also made legal prosecution less likely.

Second was WWI, which saw such an epic amount of violence and death that the supposedly gallant display of fearlessness displayed by duelists paled by comparison, and the duel simply lost all of its purported patina of glory. Suffering a pinprick while around you walked millions of men with faces and limbs blown off simply didn't carry any social cachet. And so the duel died the quiet, sputtering death of irrelevance.

Read more: The Duel in European History: Honour and the Reign of Aristocracy, V. G. Kiernan, Oxford Press, 1988

I can only speak for dueling in France, things might be different in other countries.

The last official duel in france took place in 1967 and was between Gaston Deferre and René Ribierre, two members of the Parliament. The origin of the dispute was Ribierre taking umbrage at Deferre insulting him while parliament was in session. Despite being illegal the duel was filmed and aired on france's only TV station. Mr Deferre was a well-known fencer and was used to dueling and won quite easily.

This duel became a sort of symbol for the "old way of doing things". The man who asked for reparation through duel - Mr Ribierre - was a member of the UDR political party. This party, which was basically the puppet of the General De Gaulle (liberator of France and president) suffered from a very large divide with the youth of France and more specifically of Paris. On the other hand, Deferre was a radical socialist, representing ideas which were perceived as modern and generally more "enlightened".

This duel in the mind of french youth represented the clash of the old with the new, and the new won. Thus it was often taken as an example that the old ways are backwards and that dueling is the last recourse of the idiot with no real argument (this idea was compounded by the fact that the instigating insult - "tais-toi abruti"/"shut up you idiot!" - was directly calling into question the man's intelligence.

I don't know about other countries, but for france this was a strong turning point.

Edit : one year later, in 1968, the French riots would begin, driven mainly by the youth. They got so bad the president De Gaulle felt he actually had to leave the country to evaluate his military support abroad at one point.

Edit 2: funny anecdote about the duel I forgot to add, Ribierre asked for the duel not to be to the death but instead first blood as he was getting married the next day and didn't want his fiancée left at the altar in case he lost.

If I might recommend two useful titles:

Gentlemen's Blood by Barbara Holland is a history of duelling, from the earliest times to not-long before the book's publication in 2003. It covers a lot of particulars of custom and etiquette, traditions during the "golden age" of the duel, and addresses the question of why & when it fell out of favor.

The French Quarter by Herbert Asbury (who also wrote "Gangs of New York") has a sizeable chapter on duelling as it was practiced in (mostly) antebellum New Orleans and environs.