Instead of every eighty years, it used to be every twenty years.
William Henry Harrison was elected president in 1840 and died of pneumonia one month after taking office. From that point on, every twenty years, the president who was elected that year would die in office.
Abraham Lincoln - elected 1860, assassinated
James Garfield - elected 1880, assassinated
William McKinley - elected 1900, assassinated
Warren Harding - elected 1920, died of cerebral hemorrhage
Franklin Roosevelt - elected 1940, died from a stroke
John Kennedy - elected 1960, assassinated
Ronald Reagan - elected 1980, broke the cycle by being shot but not dying.
Hopefully we will get back on track in 2020.