You have to go all the way back to 1928 for a presidential election the Republicans won without someone named Nixon or Bush on the ticket. Check it out:

1932 Hoover/Curtis LOST
1936 Landon/Knox LOST
1940 Wilkie/McNary LOST
1944 Dewey/Bricker LOST
1948 Dewey/Warren LOST
1952 Eisenhower/Nixon WON
1956 Eisenhower/Nixon WON
1960 Nixon/Lodge LOST
1964 Goldwater/Miller LOST
1968 Nixon/Agnew WON
1972 Nixon/Agnew WON
1976 Ford/Dole LOST
1980 Reagan/Bush WON
1984 Reagan/Bush WON
1988 Bush/Quayle WON
1992 Bush/Quayle LOST
1996 Dole/Kemp LOST
2000 Bush/Cheney WON
2004 Bush/Cheney WON
2008 McCain/Palin LOST
2012 Romney/Ryan LOST