An earlier comment referenced Harding, so here's a write up.
Warren G. Harding was considered successful for 3 main reasons: First he pursued an isolationist policy, which was highly popular in America at the time. Having just suffered the First World War, Washington's advice on 'Foreign entanglements' was the clarion call for politicians of all stripes, no matter how selectively that was enforced. Harding withdrew the US from international discourse, refused to join the League of Nations, and scaled back America's military. All these things were popular amongst an electorate tired of war. Second, he had the good fortune to preside over the booming 20s. America, though war weary, had come out of only a year and a half of gruelling warfare, compared to the former economic powerhouses of Europe who suffered four long years, who had spent millions on American materials. Britain had been the economic centre of the world for hundreds of years, but her control collapsed and the dollar became the most popular reserve currency. A short recession was followed by a boom that is immortalised in literature like the Great Gatsby, and Harding's tax plans, resistance to Socialism, and tariffs were credited with this success. Upholding prohibition, then a popular stance, also contributed to his personal popularity. Third, he was not Woodrow Wilson. The US was fed up with the Democratic President who preceded Harding, making him a lame duck in 1918 (by two seats), seeing Versailles - Wilson's personal crowning achievement - rejected. The 'anyone but him' principal worked strongly for Harding, who was a bland character advocating a 'return to normalcy', that is to the America that people remembered in Rose tinted glasses. Capitalising on a general sense of disaffection with what was then modern America, he promised that the USA could go back to the good ol' days. Sound familiar?
His death in office naturally buoyed his popularity – a dedicated President of the people, breathing his last breath in service to the nation he loved. He was even compared to Lincoln in terms of personality. Then the hearings started. Harding was not a morally upstanding man by the standards of time. Multiple mistresses, illegitimate children, corruption, the wonderfully named Teapot Dome Scandal, and mismanagement of Veterans affairs slowly blackened his name, until now he is considered one of the most incompetent Presidents in American history. Many historians think his economic policies, perpetuated by his Republican successors, contributed to the Great Depression, some would say his foreign policy opened the door for fascism as tariffs throttled transatlantic trade at the expense of Europe, and America turned its back on enforcing the peace it had won, enabling the rise of men who wanted that peace broken, and plunging the world in a second global war. He is blamed unfairly perhaps, for things he could never have predicted, and would not live to see, but his decisions put America on the road to financial crisis and brutal warfare, a legacy few would call ‘a return to normalcy.’
Good Sources would be 'A Companion to Warren G. Harding, Calvin Coolidge, and Herbert Hoover', a collection of historical essays, and Robert H. Ferrell's 'The Strange Deaths of President Harding' is an accessible, popular entry to the reputation of Harding.
Teddy Roosevelt held a stellar reputation after his presidency (it was widely thought that he could of, and considered, running for a third term). And he was popular enough to be included on Mount Rushmore/run on a third party platform and pull more votes then the Republican candidate. Today he is still a popular figure and has inspired many legends and colorful stories, but his legacy is somewhat mixed on account of his les than stellar legacy on race and blatant jingoism/war fever surrounding the Spanish American War and WWI. I don't think you could call him unpopular but it is unquestionable that his legacy is not as stellar as immediately following his presidency.
Many presidents images suffered following the 60's Civil Rights era as allegations of racism became more serious charges and even figures that had been seen as race positive featured some legacy damage (Teddy's was a good example, even Lincoln has faced allegations of racism due to some of the statements made in the Douglas debates as well as his support of emigrating freed slaves to African colonies).
These shifts have not always entered into public consciousness. Sometimes the legacy of a president in historical circles is wildly different from that in the public imagination.
Sources The Bully Pulpit by Doris Kearns Goodwin is a eminently readable book that deals with TR and his legacy in parts.
Looking for lincoln by Barry Schwartz. Which deals with Licolns image through time and how it has evolved.
Apologies on mobile