Graf lost to Vera Menchik in matches in 1934 (+1 -3 =0) and 1937 (+9 -5 =2); the first of these was generally regarded as an exhibition match, while the second was reportedly a women's world championship title match. She also lost a match to the problemist Heuaeker (+0, =0, -6). Vera Menchik was absent from the Semmering 1936 tournament and Graf took 1st place. Graf also played in the Women's World Championship tournament in 1937 and 1939, tying for third in 1937 and finishing second to Menchik in 1939. She was awarded the WIM title in 1950.

During the 1939 women's world championship, played concurrently with the olympiad, Graf was refused permission to play under the German flag because of her outspoken opposition to the Nazi regime; she played in the tournament under a flag bearing the Spanish word "libre" ("free"). World War II broke out during the tournament, and Graf chose to remain in Argentina after the tournament's conclusion. During her time in that country, she published two books in Spanish, "Asi Juega una Mujer" ("This is How a Woman Plays", about her chess career), and "Yo Soy Susann" ("I am Susan", about her abusive childhood).

In 1947 she married an American, Vernon Stevenson, moved to Hollywood California, and began playing under the name Sonja Graf-Stevenson. During her early years in the United States Graf-Stevenson played relatively little, giving birth to a son in 1951. However, she eventually resumed active play, winning the California Women's Championship in 1956, sharing the US Women's title with Gisela Kahn Gresser in 1958-59 and winning that title outright in 1964. By 1964 she had moved to New York and was giving lessons in the Greenwich Village chess studio run by Lisa Lane. She passed away in New York in 1965.