To persist with an argument (typically on the internet) to the point beyond diminishing returns with the persistence of idiocy. A derpbate often involves two parties (often on the internet) in mild-to-extreme disagreement repeating each others points with slight modification in response to one another. A portmanteau of "Derp" and "Debate."
Sunday, sunday, SUNDAY, watch the socially inept Randroid debate the campus Communist in the CAGE on a politics forum! You do not want to miss one excruciating line of this ten hour derpbate!