Well, the two standard ways of resolving time travel paradoxes are the consistent universe and the split timeline solutions. In the consistent universe solution the time traveller could not have managed to defeat Nixon in the first place, so that can be ruled out. Therefore the split timeline solution would apply. In the many worlds solution, by travelling back in time, he created a new branch of the time line, in which he arrives in the past, defeats Nixon, but doesn't travel back. The time line where he doesn't arrive in the past, but travels back exists "parallel" to the other one. Therefore in the split timeline resolution, there would be two timelines, one where Nixon won, and one where he didn't.
Since the two timelines in some sense form a common causal loop (although saying Nixon won because the man didn't travel back is a bit of a stretch), one sees the story line following one full iteration of that loop (which involves two times jumping back to the past; once with the time traveller, and once where there is no time travelling). Of course a loop (even if it is a double loop) doesn't have a natural end (i.e. as you correctly noticed, after Nixon winning, you could have followed the time traveller travelling back in time and defeating Nixon again), after having shown the full loop once, there's nothing new (you'd just see a repeat of the exact same events you've seen previously).
Of course if you want a more "realistic" view of the causal loop, nobody hinders you from watching the episode repeatedly in an endless loop. :-)