Sibirjak, there was a referendum in Subcarpathian Rus (now Zakarpattje) I think in 1991. People voted for autonomy (I think 72% or 78% or so were for autonomy). Ukrainian government ignored it. Well, in the context of political intimidation of Subcarpathian and Rusyn activists, ukrainization, and overall political situation in the country, demanding independence would be perfectly justified by now.
But they do not do it (yet), because their (underground) leaders know that the region is not prepared for that. Does it have capacities needed for a functioning state? Would there be a stable and relatively unified political platform that would ensure stability needed for economic growth? Would neighbouring countries accept their independence? Who would protect them from retaliation of Kiev? Russia? But being tied to Russia is really no win.
So no independence at the moment.

And Kiev ignores them practically because heeding their demands could be a catalyst for disintegration of Ukraine.

It sounds sad, if your leaders are not prepared for that today, then they will not do anything tomorrow. I think the problem isn't in a poverty of region but in Rusyn's leaders, more precisely in their absence of normal separatist leaders among Rusyns. Any peaceful appeals to Kiev are useless.. did your people send any requests to Europe? Brussels condemns the Soviet crimes, today the USSR and German nazies are same enemies for European historians and parliamentarians, and many western territories had been illegally occupied in 1939, today they belongs to Ukraine. Only your people can protect yourself against Kiev or any other occupiers, Moscow isn't a friend for you at all, more likely Washington could help you, because your region has a strategic importance for them. In the case of your independence your territory would get good money placement of military bases for example, American troops are often the companions of investment :D  Also, I don't believe, this mountainous region has no ore mineral resources, which could help you at the first time. Many countries have natural resources, but they have achieved success in a short period of time.