So, how do you find the ends of your life anyway? One end is the moment of his conception, the farthest Sam has ever been able to Leap backwards in time [when he wasn’t leaping inside someone else lifetime (having traded places with his great grandfather because of similar genetics in the Civil War episode)]
But to get a loop, one has to have two ends to tie together. In Genesis, Sam is successful at making a time loop out of his life, and it’s very plausible that by the act of making that first leap he created the other end of his life. It doesn’t matter how long Sam would have lived, had he not leaped; by leaping, he tied off the ends and therefore his lifetime no longer exists after that point.
The only time Sam leaps farther forward than the moment of his initial leap is in The Leap Back, when he leaps inside Al’s timeline because of the Simo-leap.(In the same episode, Al leaps back to a time within his own life but before Sam’s).
Additionally, in Mirror Image, Sam may have died. After the bar, he leaps as himself to Beth, similar to the guardian angel in It’s a Wonderful Leap. It’s also notable that the bar “exists” on the day of Sam’s conception, which would make his death fall at the moment of his birth. Presumably, then, in his post-Mirror Image leaps, he could travel outside his own lifetime, because he would no longer be trapped in the time loop of his life.
I think it’s quite possible that this is what the series was going for; there’s a lot of build-up to the idea/evidence that ties the arc of the series together especially in season 5.
The only upside of this is that it means Sam would not have to leap forever. Though he may not be able to go home, he could presumably move on when he had helped enough people/was ready to do so.