Sorry to play the devil's advocate, but the Church was trying to reform before the Protestant Reformation. Shortly prior to the 95 Theses, they established the post of advocatus diaboli, a job with a fascinating description: the person had to argue against another person being inducted into sainthood by exposing their faults, flaws, and flukes, to make sure that no one who was unworthy found his way into canonization. This person was appointed because there was rampant corruption and the pope wanted more credibility for the Church. Nice sentiment, but it didn't work out. Years of kerfuffle later, in 1760, a calque on the word was used in English as devil's advocate, and no alterations have been made since. Usage of the word in that form is most common, and Devil's advocate occurs more frequently than Devil's Advocate. Seems that no capitalization prevails, and the same is true for the Latin term. The phrase trended highly when an eponymous 1997 movie came out.
Hello! I'm Adam Aleksic, a sophomore studying government and linguistics at Harvard University, where I co-founded the Harvard Undergraduate Linguistics Society. In addition to etymology, I also really enjoy politics, vexillology, geography, board games, conlanging, and law.