Castro’s rule overlapped with that of 10 American presidents. Each has made noises about getting rid of him. Each has pursued policies that probably helped keep him in power. By embargoing Cuba, American policy has arguably helped Fidel.
It’s generally true that as wealth and income disperses, so does political power. People with money insist on having some influence over policy as well. It was the land barons who forced King John to sign the Magna Charta when he came to them in search of tax money in the 13th century. Those disenfranchised politically are almost invariably first disenfranchised economically. Poverty breeds totalitarian rule, whether it be rule by gangsters in ghettoes or dictators in third-world countries.
What does an embargo do? It stunts economic development. As a country's people remain impoverished, they have fewer resources with which to challenge the state's monopoly on power.
Fidel ruled for nearly 50 years. It just may be that he has US policy to thank for that.