The US was occupying Nicaragua in 1912 when TR was first defeated. That's one example I can think of.

http://en.m.wikipedia.org/wiki/United_States_occupation_of_Nicaragua

The only arguable case prior to the American Civil War would be John Adams who lost to Thomas Jefferson in the election of 1800, before news of peace agreements with France reached the United States. Although the conflict itself, or more appropriately the threat of the conflict, was a major piece of political contention it would probably be a stretch to describe it as a "major conflict". Although I would point out that James Madison's 1812 election after war had been declared against Great Britain was a very close thing, and included a revolt by a substantial portion of the Republican party.