What was the most important cause for the fall of the Soviet empire after 1989?
While it is not possible to know for sure what the most important cause of the fall of the Soviet Union was, I would argue that it was internal economic problems. I think that internal political problems would have come in a close second.
In general, the Soviet Union fell, I would argue, because it utterly failed to keep its people happy. The Soviet Union was in competition with the West, but it could not give its people anything like the economic prosperity or the political freedoms enjoyed by people in the United States and other such countries. By the late 1980s, the people of the Soviet Union were getting tired of this. They could see that their system had failed to produce the sorts of benefits that the supposedly inferior capitalist/democratic system was providing. Because of this, they came to be very dissatisfied with the communist system. This led them to want change. Their desire for change ultimately could not be satisfied with small steps that would have kept the communist system in place. This was why the Soviet Union fell.