The situation of his family, which Martin had to leave behind in Hechingen and Germany, had deteriorated more and more. Edmund Eppstein was considered intrepid and courageous. In 1938, for example, he resisted having the compulsory first name "Israel" entered for himself in the registry office, but then had to bow to coercion. In April 1942 he was deported to Izbica together with his wife Blondine, his daughter Helene, her husband Leopold Weinberger and their three-year-old grandson Moab. None of them survived.

Martin's sister Gertrud Eppstein managed to escape to New York in 1940. His sister Meta survived the concentration camps in Riga and Stutthof. She also emigrated to New York after the war.