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!
An unintelligent person or group of people who win intellectual debates through countering logical facts with insults regarding the opponent's intelligence, causing the opponent to become enraged.
Derptagonist: I saw a moving star last night! *derp*
Smart person: I highly doubt the possibility of a star millions of light-years away moving through space fast enough for it to be noticeable on Earth. I didn't hear any reports of a meteor shower, so it was probably just a satellite.
Derptagonist: Dude that's the most retarded thing I've ever heard.