"Military sources claim the plane went down in the English Channel," Leonard Nimoy explains in the episode of In Search Of embedded below, which first aired in March 1980. "Yet conflicting reports concerning this doomed flight continue to cause debate." If you don't remember Glenn Miller's music, just watch the first 2 minutes of this episode. You'll instantly recognize his standards.
Glenn's brother Herb disputes this account of the disappearance during an interview in this episode. "Why wasn't there an extensive search for the plane, especially when it involved a world famous celebrity?" Nimoy then asks. Surprisingly, this episode goes on to answer its own rhetorical question in a very prosaic way, "You have to look at it in the context of the times," an expert explains on camera, "they had a war to fight and every plane or boat they used to search was one they didn't use to fight the Germans."
Disappointingly perhaps, the show does not traffic in some of the more bizarre rumors about Glenn Miller's disappearance, including one suggestion that Dwight Eisenhower had actually sent him on a secret mission to convince some German officers to end the war early (Miller spoke German fluently), but he was captured and killed in a Paris brothel before he could contact them. His death was covered up, this conspiracy theory goes, to save the government embarrassment.
Whatever the real cause, no trace of the plane, crew or passengers has ever been found to this day. Glenn Miller is still listed officially as "missing in action."