If I remember correctly, Calvin Coolidge decided not to seek re-election because his son had passed away.
Coolidge died suddenly in Jan. 1933--before the next Presidential term ended, so he would have died in office if he had been re-elected in 1928. (Of course, the pressures of office might have brought his death sooner--just as LBJ might have died in office if he had been re-elected in 1968 rather than two days after that term ended.)