A fascinating editorial in the Jan. 23, 1908 NYT discusses how the Democratic party might want to get rid of a candidate that has been hanging around for too long:

Why should [William Jennings] Bryan get out unless he is forced out? From the point of view of the Democrat, the patriot, the wise party leader, innumerable reasons may be advanced why he should abandon his pretensions to the candidacy; from the personal point of view of Mr. Bryan, not one. Mr. Bryan is a very successful man. In seeking a third nomination he is pursuing the path of success that has led him to fame and fortune. He is a rich man. He has said that he has money enough to make him comfortable the rest of his life. He has made his fortune by being the candidate, by refusing to relinquish his grasp upon the leadership of the Democratic Party. Because of the position he holds men buy his Commoner, and lecture committees pay him large fees. Mr. Bryan, in the language of the street, has a "good thing." He would be a fool to let go of it.

Might this apply to a certain "third term" seeker today?