It was the wars in Europe ans China that won the 1940 election for FDR. He simply had more experience than Wendell Wilkie did.
I'll say again, until near the 1940 Democratic convention, Roosevelt was not expected to run for a third term. After all, it had never been done before. He had even told James Farley that Farley could run, becuase FDR would not.
Had Willkie faced some lesser name in Democrat politics, like John Nance Garner or James Farley, Willkie could well have won.
Remember, the Republican convention was in late June 1940, while the Democrats held theirs in mid-July. So the Republicans didn't know for certain who Willkie would be running against.
Willkie, an internationalist (read: supported FDR's policies), was the Dark Horse candidate. Two of his rivals -- Taft and Vandenberg were strong isolationists.
But by June 1940 Poland, Denmark, Norway, Holland, Belgium & France had fallen to Nazi blitzkrieg, and Britain was widely thought to be the next victim. So isolationism was beginning to lose some of its appeal.
Willkie favored sending all aid to the British, "short of declaring war." In 1940, that is exactly what the majority of Americans wanted.