The problem (with Communism and with answering your question) is that Communism was never implemented yet, thus making it hard to say to what degree it can be implemented at all. The most "communist" thing that the world had were different collective communities, for example the original Kibbutzim in Israel, which can at least be considered "socialist" to a large degree. On the other hand none of them were state entities, which means they were heavily influenced by a surrounding state form.

From a formal point of view, Communism can be considered one of the purest forms of democracy, which makes it susceptible to the largest problem every democracy has - the people. Any democratic society relies extremely on the people's good will, (social) responsibility, and education. That makes it also the most fragile state form possible - as soon as even one of the criteria fails, the society inevitably changes. It can be a more or less slow evolution into an aristocracy or a monarchy, or a rather revolutionary change into an ochlocracy, oligarchy or a tyranny.