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There are a couple on this list, including one host of a show for 67 years that has run for 99 years.

Weird Al? (Whose music career began in high school when he handed a demo tape to Dr. Demento.)

Patrick Moore presented The Sky At Night for 56 years - TV, not radio though

It's not exactly the same, as his shows didn't maintain a single format through their lifetime like Dr. Demento's, but Paul Harvey had a similar run.

A different type of radio program (and he also did television), but Vin Scully announced Dodger games for 67 years.