1928 Coolidge did not run.
1952 Truman did not run
1968 LBJ did not run
As I said, LBJ did run in '68. He just dropped out when his position became untenable. He probably would have done better against Nixon than his VP.
Truman actually did run, but after he got stomped by Senator Kefauver (Who he hated), he dropped out. But that was after five terms of sing party presidents.
Coolidge could have easily won in 1928, but he just plain hated D.C.