The easy answer here is 'the Second World War', though it comes with a few caveats.

Fascism as a system of government was discredited in a number of ways during the Second World War. This was partly moral - the scale of crimes committed by fascist belligerents was simply unprecedented, and implications of fascist beliefs for their potential victims became starkly clear, and meant that any effort to establish new fascist movements would be met with hostility and suspicion from groups who now realised exactly how much they risked if they let fascists gain power. As the Allies pushed into German territory in particular, they discovered more and more graphic reminders of the nature of the regime they were defeating, the nature and representations of which remain profoundly shocking to this day. It's important to remember here that fascism (and other forms of far right politics) rarely succeeded because they convinced an absolute majority of a country of their views, but rather because more traditional conservatives or centrists saw them as the lesser of two evils compared to the real or perceived threat of a left-wing revolution. After 1945, it was very difficult to view fascism as a lesser evil, and the opportunities for the far right to build influence beyond their hardcore adherents were limited, with a broad mainstream political consensus that such groups were beyond the pale.

In a more hard-headed realpolitik sense, the Second World War also laid bare the failures of fascism as a system of government. The fascist side, after all, resoundingly lost the war - for an ideology predicated on glorifying violence and the fascist state's superior ability to conduct and win wars, that they were defeated by supposedly lesser ideologies/racial enemies made it hard to maintain these views (not, of course, that various forms of apologism for Germany's military defeat didn't start to emerge quite quickly). One way of looking at the reasons for the outcome of the Second World War is diplomatic - by 1941, a large majority of the worlds governments, peoples and economic power were allied against a relative handful of fascist powers. This was no accident - it reflected the inherent difficulty of building meaningful multilateral alliances for a government system predicated on an ultranationalist ideology. It is especially telling that Nazism was unable to capitalise on widespread anti-communist feeling among many of its eventual adversaries. By the end of the 1930s, the vast majority of people in capitalist countries saw Germany as a much bigger threat than the USSR, which laid the groundwork for a wartime alliance between communist and capitalist powers that would have been unthinkable a decade before (or after). This was the cost of Hitler's seemingly successful aggressive diplomatic moves in the late 1930s - while he succeeded in forcing territorial concessions and weakening Germany's neighbours, he also made it increasingly clear that Nazism's ambitions were an existential threat on a continental (even global) scale.

All this meant that by the end of the war, both of the superpowers that emerged following 1945 were in their own way explicitly anti-fascist powers, where fascism had either little appeal (the United States) or no chance at all to emerge in the first place (the USSR). While both these sides had their own ideas about what fascism was and what made it dangerous, both saw fascists as natural enemies of their way of life.

Here's where the caveats emerge though: in having such different ideas of what fascism was and what was so terrible about it, the new Cold War dynamic did open the door for a number of regimes and political movements that were at least ambiguously fascist to survive. Perhaps the most famous such instance was the Franco dictatorship in Spain - a regime that was at the very least quasi-fascist in nature, and had relied on support from Fascist Italy and Nazi Germany to win power in the late 1930s. However, as Franco was also highly traditional, religious and anti-communist, in the eyes of the Allies (especially Britain and to a lesser degree the United States), Franco did not embody what they thought fascism really was (eg totalitarian, atheistic, modern), and was instead the kind of traditional authoritarian conservative they could do business with. This meant that the Franco regime was able to survive the end of the war despite being seen as fascist by the USSR (and the global left), and by the 1950s the Franco regime had positioned itself as an important anti-communist ally in the Western Mediterranean, allowing it to survive until Franco's death in 1975. Similar Cold War dynamics saw the US supporting regimes that were at least ambiguously fascist in nature, such as Pinochet in Chile.

Equally, ambiguously fascist movements saw some success in various democratic countries from the 1970s onwards. By rebranding themselves, losing a lot of the traditional 'fascist' iconography and latching onto new, racially-charged issues such as immigration, it proved possible to build new movements that left behind at least some of the stigma of the 'fascist' label. Groups like the Front National in France played into the ambiguities of what fascism 'really' is to successfully tap into similar veins of social, racial and cultural anxiety that had fuelled fascism in the interwar period. The FN and other comparable movements reflect the ambiguity of the defeat of fascism in 1945 - these movements succeeded by explicitly distancing themselves from the symbols and language of the 'original' brands of German or Italian fascism, and it's difficult to imagine that they would have succeeded if they hadn't, in that any party that actually used a swastika for a symbol and praised Hitler would soon find itself a pariah (which has generally proved the case for the groups that did actually try it). But this was arguably a cosmetic victory rather than an absolute victory over the ideas that fascism embodied - it's quite possible to hold, I think, that the fascist aesthetic was defeated in 1945, but the underlying ideology never quite went away, and rather adapted itself to new discourses and contexts.