Under the Confederate Constitution (
https://avalon.law.yale.edu/19th_century/csa_csa.asp) the President was appointed for a term of six years (Article II, Section 1 (1)). At the end of that term the President was ineligible to be appointed again as President, or Vice President [no puppet masters in the Confederacy].
Although the CS Constitution largely copied the US Constitution there were some differences, the Presidential term being one. Davis explained that particular difference in
The Rise and Fall of the Confederate Government where he said:
"The official term of the President was fixed at six instead of four years, and it was provided that he should not be eligible for reƫlection. This was in accordance with the original draft of the Constitution of 1787."So, had the Confederacy fared better, at the end of Davis' six-year term it would be time for someone new. Had the war finished with the Confederacy sustained, I suspect that there would have been a big call for R. E. Lee as President but I'm not sure he would have agreed to it. In which case I think Stephens would have become Confederate President. As an experienced politician and Vice President for a successful Confederacy he would have been difficult to defeat.