Any reason besides Autarky?
Well, no, just autarky. Of course, a lot depends on how the war ends. Is this Nazi Germany self sustaining or, as much as they dislike it, they need to import stuff Latin America exports? Even in that case, I hardly see Nazis approaching Latin America, considering they'd see natives and mestizos as a lesser race. They may try to diplomatically engage the "whiter" parts of Latin America (ie, the Southern Cone), but they'd be reluctant partners at best. At "best", and depending on the state the UK leaves the war and if Nazi Germany remains a net food importer, I'd see an Argentina trying to rely on Germany to (fail to) fight American influence in South America like they'd often tried under the British umbrella during the first half of the 20th century. But it boils down, a lot, to the Nazis interest in trade, or the lack of such, and the state in which the British Empire is after the war.
I'm not mentioning the Holocaust as a factor because most of the worst of it may remain unknown or rumored (Nno Eisenhower making people take tours to the concentration camps IITL) and because IOTL, Stalin and Mao's atrocities never interfered with realpolitik