Before that the only real cases are William Henry Harrison in 1840 and Grover Cleveland in 1892 (and he was a former President who had a plurality of the popular vote in 1888). Andrew Jackson won in 1828 after losing in 1824 but that was in the interval between the end of the first party system (Federalist vs. Republican) and the rise of the second party system (Whig vs. Democrat), and the winner of that election had to be selected by the House of Representatives.
The elections before 1804 don't count because the second-highest vote-winner became Vice President.
That's a very interesting point. But how many times did a candidate who had earlier lost an election even bothered to come back and try again? Nobody other than Nixon comes to mind, but Walter Mondale and Bob Dole are two guys who have pulled off the unusual "exacta" of losing once as a VP candidate (Dole in 1976 as Ford's running mate and Mondale in 1980 on the Carter ticket) and later as a presidential candidate (Mondale in 1984 and Dole in 1996).
I’m still counting Reagan and G.H.Bush .
They ran to get nomination and lost then later came back and won.
See your points though. Especially earlier yrs.
Lincoln was anti war and Jackson was pro war.
Lincoln like most republican believers back then were against Spanish American war.
Lincoln countered that he supported the troops because he voted to provide them boots.