The nomination process for US presidential candidates favors incumbents. This seems also to be true for Vice Presidents (e.g. George H. W. Bush, Gore). Have any Vice Presidents not been nominated although they ran tried to be?
The most recent sitting VP not nominated while running for President was Alben Barkley, Truman's VP. He was passed over for a younger man (Adlai Stevenson) in 1952.
Also Thomas R. Marshall, Wilson's VP (1920). In the 19th century, the Vice Presidency was considered as spot for "has-beens and never-wases".