While the Founding Fathers identified the need for a line of succession of power, they failed to dictate important details pertaining to the ways in which this would happen. For example, who has the power to declare a president unfit to serve, when and how the president should return, and if the VP should continue out the remainder of the president's term.
It wasn't until the assassination of JFK that Congress passed the 25th Amendment to lay out a protocol for what would happen in the case of the death, resignation, incapacitation, or disability of a president or vice president.
George Washington was actually the first president to suffer health challenges while in office. Disease ran rampant in the late 1700s and the first president underwent surgery for a tumor and suffered from a serious bout of the flu while in office. Luckily, he survived both health threats but later date of a throat infection once he left office.
Other presidents that had health issues while in their role were William Henry Harrison (the shortest-serving president who died just 34 days into just presidency from pneumonia), Grover Cleveland, Woodrow Wilson, Franklin D. Roosevelt, Dwight D. Eisenhower, Ronald Reagan, and George W. Bush.