There are numerous points in time and overlapping events we could call death knells in actual multi-party representation. The civil war and Lincoln's "Americanism" destroyed any actual sense of real opposition in the political leadership. "These United States" became "The United States" - a country with a strong centralized government and the states as subordinate provinces. You could talk a good game about our freedom and fighting back against whatever they were imposing, but from that point on everyone knew you couldn't actually back it up with force if necessary. You had to be the loyal opposition. This naturally filtered out anyone who wasn't going to play the game.

Then you get into a lot of the unconstitutional economic shit that's above my head, but was no doubt easier to pass since the politicians no longer represented the people and were more easily bought out. This includes the Income Tax and the Federal Reserve. (someone needs to tell me how they managed to get so many states to agree to the income tax though, because I don't see that happening today)

Rebellious and independent sentiment was still alive within the states themselves for a long time, as people still believed what they were taught about the constitution and states rights. That was until the Civil Rights Act got passed, and schools were forced to integrate by the military. This meant that not only did Governors have to follow federal law, but individuals and businesses no longer had their own freedom of association. Everyone now felt the loving reach of Uncle Sam. You'd think that means people would become more united against the government, but...

Mass media had already been bringing the nation together into single competing ideologies (rather than individual self-interested state factions) for a while at that point, and more individuals at the local level were able to get involved in the process than ever before. Various constitutionalist groups who pointed out that neither party was following the founding principles any more - and worse yet might be influenced by international communist ideology - were gradually gaining support. The "two-party" system couldn't allow this. Controlled opposition figures like William F. Buckley were put in place and amplified by the media to dampen any kind of actual groundswell opposition. (the John Birch Society was one, but the pattern has repeated many times since then with backing of the intelligence agencies) Rather than people being encouraged to build coalitions from the ground-up and vote their conscious, the media always held up third-parties as spoilers to keep people locked into the "two-party" system.

Obviously there's a lot more to it, like how wars were exploited to strengthen the military industrial complex, influential wealthy cabals of rootless globalists, clandestine oversight of the parties, and punishing politicians who strayed too far off the ranch. Good lord it's times like this I wish we had 'Based AI'. A legit chatbot should be able to generate a much better answer than that, with sources... but if you asked any major model this question today it would parrot off some bullshit about progress and gay rights and how the uniparty is a baseless conspiracy theory.