The Second Diaspora of the Jews came in the 21st century when the State of Israel was finally defeated by its enemies, barely a century into its existence. While millions of Jews remained and became subjects of an Islamic Palestine, more fled, and took up residence in other parts of the world.
Almost immediately, these refugees developed an organization called the Second Irgun.
A Second Diaspora is also implied to have taken place in "Les Mortes d'Arthur," where a similar Second Irgun is among the story's many antagonists. Harry Turtledove has not made clear whether "Mortes" and "Next Year in Jerusalem" are part of the same timeline.