In 1939, Eliskases emigrated to South America. He played under the German flag at the 1939 Buenos Aires Olympiad, during which World War II began, when Eliskases (along with many other players) decided to stay in Argentina (and for a while in Brazil) rather than return to Europe. During those years he struggled to make a living; and in Brazil he was threatened with internment and expulsion, though some Brazilian chess enthusiasts helped Eliskases avoid that fate by hiring him as a chess teacher.