The Ukrainian hockey was pretty much doomed in 1991 after the collapse of the USSR. This was the turning point. People, who think that the decline is a recent event, are simply NOT familiar with the subject.
The Ukrainian hockey got its life in the early 60s when Sokol Kiev, the first Ukrainian (within the realm of the USSR, of course) professional hockey club, was founded. All players and coaches were exclusively from Russia (or Russian Soviet Federative Socialist Republic then). Another professional club was formed in the late 70s in Kharkov via the same approach: all coaches and players were from Russia. So, basically, the Ukrainian hockey was thriving, so to speak, thanks to constant injections of talent from Russia and state support. Eventually, by the mid 80s, Ukraine started producing some home grown talent like Khristich, Zhitnik, Godynyuk (see more interesting info on him below), etc. By the way, now it should make sense (to those not familiar with the topic), why the vast majority of Ukrainian players are from Kiev and Kharkov.
But when the Soviet Union collapsed, everything has drastically stopped: development of future home grown talent, injection of players and coaching from Russia, and, of course, the state funding. It has been a downhill motion for the Ukrainian hockey since then. The reason why Ukraine was fairly competitive in the 90s (and maybe slightly beyond) is because it was "riding" on some of its talent grown earlier. Once the "fat was burned", there was nothing left.
P.S.1. Please don't nitpick about the term professional in reference to the Soviet sport. Yes, technically, there was no professional sport in the USSR, but, factually, athletes were making money.
P.S.2 Godynyuk played a supporting role in a Soviet youth flick "Troika" (referring to the hockey term "line"). The movie was filmed in Kiev, the capital of Ukraine, and local kids from Sokol Kiev youth squad took part in it. The mid 80s was the absolute peak of the Ukrainian hockey.