It died with the Cuban revolution and Soviet support for Castro. Didn't it?
It died with American leftists’ support for Communism in Latin America. The left - including the entire Democrat party - then by default ended up defending any foreign intrusion that assisted in the spreading of Communism (the Soviet Union, for example). They also ended up supporting guerrillas and various destabilizing movements that destroyed these budding economies and created the climate in which people see the left, with its airy promises, as a savior. And of course the Dems and more radical left loved the ethnocentric policies of these groups, which pit the various Latin American indigenous or Indian groups against Latin Americans of European descent.
The left has done enormous damage to Latin America. But the problem is that since this left was not only the radical left, but our very own Democratic Party, with luminaries such as an ex-president, Jimmy Carter, we have been unable to deal with Latin America realistically and exert any effort to defend our interests there. Look at how the Dems in Congress are trying to prevent aid to Colombia, which is one country in which we have had some success in defeating a radical movement (although only since Bush has been in office - Clinton handed off most of the country to FARC).
So the big problem with the Monroe Doctrine is that the Democrats don’t support it, and in fact actually want Latin America to be our enemy.