Even in an apocalypse, would the gods still have children? What would stop them? The gods continued to have kids when the Flare hit and of course some surviving demigods had some kids. After the apocalypse hit demigods and legacies continued to live, struggling to survive with the Cranks and WICKED. Tons of demigods were taken by WICKED to find a cure. Most demigods now don't even know what they are, just gifted or cursed with abilities most people don't have.