Well, the Glorious New Imperium of Outer Mongolia is unlikely to go away any time soon. It seems to be a threat to no one but its own people, who must, certainly, have their faces all trapped in a rictus of terror. On a geopolitical level, however, Mongolia serves as a useful buffer state between the Soviet Union and the Greater East Asia Co-Prosperity Sphere. That way, there is only the (relatively stable) in Transbaikal. I can assure you that, were the border to extend further, war would become much more likely between those rivals.
You can say a lot of bad things about the Sternbergs, but they seem to be reliably neutral in world affairs. I like to think that, if the West continues to bring humanitarian aid and assistance there, the situation may change - but who's to say? Perhaps, someday, totalitarianism in Mongolia will fall like it has in some of the crazier socialist states of Europe - actual democracy may be too much to hope for, but at least some kind of more enlightened dictatorship.