How popular...

[J. J.]

William McKinley 4
Theodore Roosevelt 5
William Taft 2 (possibly 1)
Woodrow Wilson 3
Warren Harding 2 (especially toward the end)
Calvin Coolidge 4
Herbert Hoover 1

Of these six, two died in office and the third became seriously disabled.  I would expect that barring that, I would expect Mckinley, Roosevelt, and Coolidge to have won re-election, had the won.  Taft, Hoover lost re-election and Harding probably would have.

A healthy Wilson is a question mark; could he have won in 1920?  Very possibly.

[J. J.]

McKinley did win re-election. Or do you mean for a third term?

1904, a third term.  It actually stunned many people when TR declined to run in 1908, which would have given him about 11 years in office.

[J. J.]

What do you base his popularity on?

As I said, the national mood. I read about our Presidents and their connection with our nation's mood, then I make the assumption of if they were popular or no.

McKinley went to war, the nation wanted war, he was popular.

Harding promised "Normalcy", the nation wanted "normalcy", so he was popular.

Taft did not appease TR enough, the nation loved TR, so Taft was unpopular.

You are forgetting Teapot Dome.