The economies of Latin America aren't diversified like North Korea and when the massive sanctions come would utterly implode. It doesn't take a genius to realise that when your country's main export is coffee (or copper, or bananas, or whatever) that when nobody wants to buy your product (because your country is a horrible abuser of human rights) and the price of said product has gone way down for one reason or another (natural economic fluctuations), that you are utterly screwed economically and you'd get a civil war where the United States is backing the opposition. The very fact the United States is there and has always seen Latin America as its backyard will make things very difficult. Also, the ability to develop nuclear weapons (North Korea's greatest asset) is going to be limited.
This would probably have to be a regime emerging from left-wing forces, since your right-wing Pinochet, Somoza, etc. types have to answer to the United States, not to mention how rogue state status is very bad for business, thus they'd inevitably get removed by the elites in their country or in the United States. Although if you went back far enough I could see some sort of Falangist-esque clerical fascism thing emerging which could co-opt a lot of support which would otherwise be socialist and still be palatable to the elites. There's still the economic issues which make it very difficult to evolve into a North Korea-type state, and not to mention the issue of the United States. If North Korea had no counterweight to the United States, it would've been gone decades ago. Who will defend our Latin American Falangists from the US? The only real option is Nazi Germany after a victory in WWII, who would support this country as a means of power projection and such. Obviously this country would play up the national socialist/fascist angle of their ideology to appeal to the Nazis in this time. But the question is--can this country resist constant meddling from the United States and American-supported neighbours, and can the Nazis successfully be to them like the Soviets were to Cuba?