In some cases the issues were minor, in other cases quite grave, and sometimes it took decades for the public to learn the truth.
Pandemics have cursed the presidencies of both the current president, Donald Trump, and Woodrow Wilson.
Each played down viruses that killed hundreds of thousands of Americans.
Both presidents became ill – and each had to decide how much to tell the public.
Like many administrations before him, the White House tried to keep Wilson’s sickness a secret.
The president was at talks in Paris on ending the First World War when he fell ill in April 1919.
His symptoms were so severe and surfaced so suddenly that his personal doctor, Cary Grayson, thought he had been poisoned. After a fitful night caring for Wilson, Grayson wrote a letter back to Washington to inform the White House that the president was very sick.
Flash forward 100 years. Mr Trump told the world that he and First Lady Melania Trump had contracted Covid-19 in a tweet at 12.54am on Friday.
The White House initially shared few details about his condition. White House press secretary Kayleigh McEnany said he was taken to Walter Reed National Military Medical Centre “out of an abundance of caution”.
It was a startling twist for Mr Trump, who has been telling supporters on the presidential election campaign trail that the nation had turned the corner on the disease, which has killed 208,000 people in the United States.
Mr Trump said he played down the pandemic so as not to create panic, but there were political reasons for doing so. Seeking another four years in office, Mr Trump did not want the US economy to tank before the November 3 election.
“The Wilson administration, for a very different reason, completely downplayed the pandemic,” said John Barry, an adjunct professor in public health at Tulane University whose book The Great Influenza chronicles the 1918-19 pandemic that sickened Wilson and killed 675,000 Americans.
“Wilson was concerned that any negative news about anything would detract from the war effort – decrease the energy that people would put into winning the war. In this case, there are more strictly political benefits.”
William Howell, professor of American politics at the University of Chicago, wonders how transparent the White House will be about Mr Trump’s case of Covid-19.
“He is obviously going to be eager to get back on to the campaign trail,” Prof Howell said. “He has all kinds of incentives to signal strength and to get back into the mix. He’s going to want to.”
But he added: “This is a president who’s been less than straightforward over the course of his presidency about all manner of factual issues. And so, is he to be believed is a good cause of real concern.”
He said the pathology of Covid-19 and the virus in 1918 is “very, very similar. Very similar, and that’s a little scary”.
History is replete with examples of how presidents have kept the American public in the dark about their ailments and medical conditions.
President Grover Cleveland, fearing poor health would be a political weakness, underwent secret oral surgery late at night on a private yacht in Long Island Sound.
The cancerous lesion taken from his mouth was displayed in 2000 in an exhibit by the College of Physicians, a Philadelphia-based medical society.
President Lyndon B Johnson secretly underwent surgery for removal of a skin lesion on his hand in 1967.
After leading the nation through a decade of war and depression, Franklin D Roosevelt was diagnosed early in 1944 as suffering from high blood pressure, hypertensive heart disease, cardiac failure and acute bronchitis.
The problems also betrayed an underlying arteriosclerosis – hardening of the arteries.
Roosevelt was put on a low-salt diet and ordered to cut down on smoking. But with an election coming on, Roosevelt and the White House staff issued a statement saying the problem was far less serious.
“The stories that he’s in bad health are understandable enough around election time, but they are not true,” his doctor told a reporter.
Historians now believe his doctors concealed all the facts from their patient and the public.
Roosevelt won re-election. Only months later, on April 12 1945, he died of a stroke.
According to historian Robert Dallek, President John F Kennedy suffered more pain and illness than most people knew and took as many as eight medications a day, including painkillers, stimulants, sleeping pills and hormones to keep him alive.
Mr Dallek, who wrote a biography on Kennedy, examined medical files from the last eight years of Kennedy’s life before the president was assassinated.
As president, Kennedy was known for having a bad back, and since his death, biographers have pieced together details of other illnesses, including persistent digestive problems and Addison’s disease, a life-threatening lack of adrenal function.
Kennedy went to great lengths to conceal his ailments, even denying to reporters that he had Addison’s disease.
President Dwight D Eisenhower had a serious heart attack in 1955, while on holiday in Colorado. He was admitted to hospital for six weeks.
Instead of advising Eisenhower not to run for a second term, his doctor recommended that more time in office would aid his recovery.
In 1841, William Henry Harrison became ill with what doctors thought was pneumonia caused by cold weather during his inauguration, where he rode horseback sans topcoat. The White House did not tell the public that Harrison was sick. Harrison died just nine days after becoming ill and only one month after taking the oath of office.
After pools of reporters began to cover nearly every moment that a president is in public, it became harder for commanders-in-chief to keep their medical conditions private.
The first known instance of a so-called pool reporter inside the White House was in 1881 when James A Garfield was shot. As he lay in bed, Associated Press reporter Franklin Trusdell sat outside the president’s sick room, listening to him breathe and sharing updates with other correspondents.
“I listen for every sound,” Trusdell wrote to his wife in a note about his overnight Garfield watch at the White House. “A dog barking in the distance is heard. A fountain splashes on the lawn. Not a step is heard in the mansion. The president sleeps.”
