The Hungarian Soviet Republic started falling apart after the Soviet capitulated to Clemenceau's ultimatum in mid-June, that entailed giving up all territories regained up till then in the impressively successful Slovakian campaign, in exchange for Romania vacating a large portion of land they had acquired and a ceasefire all across the front. This was a catastrophic error - though only in hindsight - and was single-handedly the greatest contributor to eroding the morale of the Hungarian Red Army as the soldiers lost all will to fight and were no longer a cohesive army after that, even those who didn't defect en masse. Without the benefit of hindsight, one could see why the Hungarian government accepted it - but as it turned out, the Entente and Romania immediately reneged on their promises and Romania invaded anyway.
Without Romania being attacked by the Soviets, there is really no way for the Soviet Republic to survive for a whole year. The Entente had every intention of extinguishing communism from all Eurasia. Having the government defy Clemenceau's ultimatum will probably lengthen the military resistance, but not for more than... three months, I'd say (the economic issues ravaging the country, simply as a result of being wartorn and blockaded, would probably have led to a general collapse in winter, I'm guessing). So we basically need to cheat - organize a massive general strike in France, enough to have the French divert resources that would have been used to supply an offensive into Hungary. Of course, the Soviet Republic also needs to stay defiant - there was actually a pretty sizable grassroots communist movement in the Soviet Republic, but most of the soldiers probably still fought partly or fully out of patriotic fervor, not so much communist internationalism. The Soviets then need to attack or at least seriously threaten Romania. This is going to be a bit harder, since the French were already giving up on Denikin in Ukraine by the end of April, 1919, which was pretty early during the Soviet Republic's life. If we move our aforementioned general strike to just after March 21 (perhaps inspired by news of the Hungarian revolution, French workers go on strike in solidarity? The strike can't happen before March 21 as the only reason the Soviet Republic could form the way it did is because the previous government surrendered power to the socialdemocratic-communist coalition after the French issued the "Vix-note" on the 20th - a move they would have delayed if there had been troubles on the home front), perhaps Denikin still gets a tiny bit less support and the Soviets can defeat Denikin and threaten Romania a bit sooner. At any rate, just find some way to handwave a credible Soviet threat that persuades Romania not to make any more moves against Hungary, and the Soviet Republic can limp along for a bit more, enough to sign ceasefires with all its neighbors. It's probably going to get overthrown eventually, though, unless Hungary can hold onto a secure line of supply to Soviet Russia through Carpatho-Ukraine - which also requires better Soviet performance in the Polish-Soviet War.