While Japan under Taisho was arguably very liberal, with a free press that could even promote republicanism, as well as public suspicion of the military after the Taisho Political Crisis, the first election to the House of Representatives with man suffrage took place in 1928, 3 years after the passage of the General Election Law. While the Peace Preservation Law was also passed at the same time, that some would argue as the end of Taisho democracy, and that some Communist groups were banned, communists and syndicalists could actually form themselves into new groups or ran as independents and won seats as late as in 1932. Party-rule indeed came to the end on May 15, 1932 when Prime Minister Tsuyoshi Inukai was assassinated, not when Hirohito became Emperor. From 1932 until 1946, the majority party leader in the House no longer became Prime Minister.
To have Taisho Democracy sustain, however, you may need a much early POD, better making the Great Depression less severe to Japan. However, that would be borderline ASB, so the best would be preventing the death of Hara Takashi. However, Takashi did not push for man suffrage in our time, he just simply lowered the requirement to become a voter. Perhaps he would eventually do it had he lived longer, but I doubt his sincerity in pushing forwards man suffrage.
One of the major reasons in support of the GEL of 1925 in OTL however was that the military junta that temporarily took over in the early 1920s screwed up too much during the Kanto earthquake, so that party politicians in both houses including the Peers at the time decide to unite against the military in order to prevent another military takeover. Bear in mind that the military prime minister died immediately before the Kanto earthquake, leaving Japan with no prime minister during the crisis, while when the aging Yamamoto Gonnohyo took over, it was already too late. There were rumors that the entire cabinet has been eliminated by the earthquake, or that Korean Japanese were trying to burn down buildings and rob the Japanese, leading to race riots after the earthquake. Despite the martial law, the whole Kanto region was simply under the state of anarchy.
The best way for Taisho democracy sustain would be the Seiyukai government under Hara Takashi sustains until 1927, making him the longest-serving prime minister. He will be pushing forward the idea of peaceful economic expansion like the post-war LDP. As a highly effective and careful politician, the Kanto earthquake would be an opportunity instead of disaster for Hara. Hopefully man suffrage could he passed in TTL for other reasons, say pressure from within the ruling Seiyukai, or that Hara decided that it would be better for him to introduce man suffrage to save his declining popularity. When the first general election using man suffrage was finally held in 1927, the more liberal Kenseikai would be swept to power after 8 years of Hara rule.
Wakatsuki Rejiro should be leading the Kenseikai at the time, since OTL PM and more competent Kato would have died by then. The Showa Financial Crisis broke out, and Wakatsuki screwed up like in OTL, leading to his assassination and a military takeover. The military junta will be a caretaker government appointed by genro Saionji to fix things, but when the real Great Depression came, the military caretaker regime would screw up more than the OTL Minseito government. Riots would take place, but not from far-right nationalists. Far-left syndicalists and Communists would try to stage a revolution, while far-right militarists would be pretty much fucked and demoralized.
When the election would be held in 1930, genro Saionji would decide that he better appoint the majority party leader again, this time Kisaburo Suzuki or Ichiro Hatoyama should become PM, since I don't see Inukai joining the Seiyukai in TTL. The Left would win far more seats than in OTL, but would be divided between Christian socialists, social democrats, syndicalists, pro-Soviet snd anti-Soviet communists, so Kenseikai should at least remain the second largest party.
This time, Seiyukai would not have the majority of seats given the rise of the left, and there would be a grand coalition with Kenseikai to tackle the economic crisis. However, one thing is for sure, the military would be severely weakened, and the new government would be forced to introduce labour-friendly policies due to the national shift to the left. There will he cuts, but this time it would mainly be military cuts. With the post-war elites combined together in this way, we may well see speedy recovery without the need of military takeover again by the mid-1930s.