The downfall of Communism in Russia was not due to the lack of elites. Indeed, after the old elites were driven from power, new ones quickly rose to take their place. Communist party bureaucrats became the new ruling class.
Apologists for Communism often point out that this wasn't true Communism, and so Communism didn't technically fail, and they have a point. I would argue that Communism still failed in the sense that it didn't account for human nature.