In OTL, TR issued a statement immediately after the 1904 election:
"On the 4th of March next I shall have served three and one-half years, and this three and one-half years constitutes my first term. The wise custom which limits the President to two terms regards the substance and not the form. Under no circumstances will I be a candidate for or accept another nomination."
https://books.google.com/books?id=6PkcAQAAMAAJ&pg=PA627 His supporters in 1912 argued that, as the *Outlook* put it, "When a man says at breakfast in the morning, 'no thank you, I will not take any more coffee,' it does not mean that he will not take any more coffee to-morrow morning, or next week, or next month, or next year."
https://books.google.com/books?id=1JJFAQAAMAAJ&pg=PA616 This analogy was much ridiculed, and gave rise to this cartoon:

There was simply no need for TR to commit himself on this in 1904. Suppose he had kept quiet, and then accepted the nomination in 1908, saying it was really his "second elective term"--an approach he had so unnecessarily ruled out in 1904. He would have had very little trouble getting re-nominated in 1908--even Republicans who disliked his progressivism knew that their party could win with him, and were unsure it could do so with another candidate. And I don't think he will have much trouble defeating Bryan. The question then is what happens in 1912. Then TR will not be able to run again without expressly violating the no-third-term tradition. There could be no sophistries or excuses about second elective terms, no room for argument that the tradition only applied to consecutive terms, etc. He would have to flatly say that the tradition was wrong, or at least obsolete--and this in a time of peace (unlike 1940). Would he do so, and if so would voters follow him? Or would sixteen years in power lead to too much wear and tear on the Republicans, even with TR as their leader?