I've thought about it quite a bit, but I think it's just not feasible for them to survive in the long run, especially when Horthy makes a return with his loyalist troops and starts retaking the country.
While the Hungarian Reds did occupy a lot of territory fast, they were cut away from both Soviet Russia and the Bavarian SR, making their backing by said potential allies extremely difficult. The regime didn't have universal backing from the Hungarian populace, since it was installed in a coup. The puppet SR here in east Slovakia had even less sympathizers (though people in the big cities at first welcomed Red troops, but only because they mistook them for standard republican or royalist troops). The Reds were very heavy-handed in handling dissent. The Red Terror in Hungary didn't do them any favours. Also, several violent retalliatory actions against locals in Košice needlessly undermined the effectiveness of the occupation in east Slovakia and the survival of the SSR puppet. Given that Košice and Prešov were both strategic assets for the puppet state, pissing off the townspeople was an incredibly short-sighted move by the occupiers.
After Horthy's return with anti-Red troops to Hungary and the combined Entente and Czechoslovak Legions operations in Slovakia, defending the captured territory proved extremely difficult. The thing about the HSR and the puppet is that both were very provisional in their nature. Of the two, the HSR was a bit more organized, of course, but its overall state was still that of a country undergoing a revolution, not one with a finished consolidation of power and infrastructure in the hands of the new regime. Add to that the fact that Hungarian citizens were fed up with the regime within a mere few months and questioned its rise to power (coup, then the red terror against dissenters), and you've got a steadily decreasing approval rating for the regime.
There was a plausibility check thread about the Soviets sending help to the HSR -
see here. Frankly, I think the Soviets had bigger fish to fry than help the HSR, mainly because of the inappropriate timing (the Russian Civil War was alive and well and from decided in 1919). Complicating matters even further, Kún despised Russian communists, since he regarded Russians as barbarians who didn't deserve communism and weren't ready for it. This further widened the gap in the HSR between those who were for an alliance with the Soviets and those who hawked self-reliance of the HSR. With such an amount of differences, it's no wonder the HSR was relatively easy prey for a counter-coup and loyalist retaking of the country.
I don't see it happening. The reason they got into power was because they rejected the treaty of Trianon. That means they WILL fight the Romanians in Transilvania. The Hungarian army was in terrible, terrible shape, whilst the Romanian one had spent two years preparing for this moment.
Assuming the stars align and the Hungarians somehow stop the Romanians, the French might very well intervene with their forces in Serbia.
That too. Thanks for bringing that up.
TBH, the HSR's main failings was that it wasn't diplomatically cunning enough, it acted arrogantly towards both its own citizens and foreign governments and it tried to do too many things at once (land grabs, collectivization, plans for spreading the revolution, etc.) without any realistic assesment of where and how they'd get their funds from and how they'd repair or replace their ramshackle military and economic infrastructure.
