Presidential rematches are pretty unusual in American electoral history, especially in the post-bellum era.
Usually, the defeated candidate is so politically damaged that they do not seriously consider another Presidential run.
The victor is by definition the incumbent, and usually in a stronger position the second time around.
Someone interested in a rematch has to contend with the fact that their own brand has been tarnished and that their opponent will likely be in an advantageous position. Rematches and post-Presidential political careers were more common in the early Republic, but seem to have almost entirely disappeared.