A guy like TR, who ate the right side of a Denny's menu every morning before wading into malaria-infested rainforests, was not likely to live long past sixty.
However . . .
This is technically possible, and not quite as crazy as it might sound at first. In 1940, Teddy would be 82 years old. Old? Certainly. But not much older than Churchill was when he returned to the premiership (77), or Joe Biden and Bernie Sanders will be next year (78 and 79, respectively). Adenauer stayed as Chancellor of West Germany until he was 87! These are just the examples off the top of my head. And his daughter Alice did live to be 96 . . .
If someone writes a timeline where Teddy somehow lives to be that old and becomes both the oldest and youngest president in history, I'd freakin' love it. So someone should write it. Teddy goes on the Keto Diet, I don't care how you make it happen, it sounds like a blast.