I think that there could be a variety of different answers to this question. On one hand, I think that the sincere and genuine fear that each side held towards "the other" enabled the Cold War to go on for so very long. Leaders entered into the position of power with the firm understanding that the people shared, or were told to share, and that the governmental complex all understood in that "the other" was to be feared and stopped. Stalin's and the Soviet development of the Eastern European Bloc of nations as well as satellite governments made it clear that Churchill's warning of the Iron Curtain was accruate. At the same time, Truman unified the Central Intelligence Agency, the Department of Defense, and the National Security Council for the sole purpose of containing Communism. Both sides understood that their function, as political and military entities, were committed to stopping "the other." The construction and organization of political orders and social orders were predicated on the other side being stopped or eliminated.
In a larger sense, though, the Cold War continued for so long because there was clarity in this structure. Governments from both nations benefited in a structure where the adversary was clearly defined, and where each person understood their fundamental function. With such a clear adversary, politicians were able to mobilize people into submission and adherence in a clear manner. There was little debate as to the threat of the other if the constant fear of a world taken over by Soviet oppressive communism or American decadent capitalism. Both sides operated with this clear threat and the direct result was the sustenance of political power for decades. Political candidates and leaders were primarily defined by their stance against the other and if they could navigate this well, political success would be theirs. In this, there is a vested interest to continue the Cold War in that the "script" to follow was an easy one, guaranteeing some level of success and ensuring public obedience would follow.