Little remembered, but Harry Truman wanted to run for the 3rd term in 1952. He was so unpopular that defeat seemed likely, especially after Ike declared as a Republican candidate.
Estes Kefauver defeated Truman in the NH primary in early March. Machine Democrats despised the reformer Kefauver. Truman persuaded the reluctant Adlai Stevenson to run.
Truman wasn’t on the ballot, whether he wanted to run or not. You don’t have to go back to ‘28 to find the situation that we are in now.