When has the us had republican presidents for three terms?

The longest a republican has served as U.S. President is 8 years (two full terms). They are...

Ulysses S. Grant (1869-1877)

Dwight D. Eisenhower (1953-1961)

Ronald Reagan (1981-1989)

George W. Bush (2001-2009)

Presidents Eisenhower, Reagan and Bush the Younger were/are prohibited by the 22nd Amendment from running for a third term. Pres. Grant ran again in 1880 but failed to get the Republican Party nomination (which went to James Garfield).