Castro's rule in Cuba has been relatively uninterrupted because of being "the only game in town." He has used the strength of his own personality as well as the force of controlling all aspects of the executive branch to ensure that dissent is swiftly punished. In controlling state owned media that allows his own image to be glorified without opposition, this has further allowed his own administration to be in office without credible challenges to it. As he has been in power for quite a while, there are generations of Cubans who have known nothing other than "Fidel's rule," which helps to add continuity as a reason for his persistence.
Well, his is a dictatorship which controls the media, the economy and the political system. It does not allow dissent, except sometimes for show. He has hundreds if not thousands of political prisoners, and has sent many of his criminals and opponents to the United States. Some people also suggest he has a very effective intelligence network among Cuban exiles living in the US.
But the largest reason for way he has been able to stay in power is, in my opinion, US foreign policy towards Cuba and the embargo. Since it economically hurts the people there, he can blame every economic ill there is (including those caused by an inefficient and outdated socialist system) on the United States. He makes a great show of demonizing the US at every turn, and for the most part, people believe him.
This is really a matter of opinion, of course, but I can identify a few possible reasons why it has lasted.
- Repression. Many regimes, like that in North Korea, can last a long time simply by being harsh enough to prevent any real dissent from arising.
- The fact that Castro was highly respected for bringing to an end a repressive regime that ran Cuba before he took over.
- The fact that Cuba has done okay in a few areas, such as health care and sports. These make Cubans feel good.
- Nationalism. Castro has done a good job of selling his way as a response to Yankee imperialism. You can argue that our embargos have helped.