It was an unwritten rule basically that you didn't run for a third term (the Washington precedent). A couple did consider it but only Franklin Roosevelt did it, then got elected for a fourth. After that, the Republicans got an amendment passed that from then on limited the President to two terms. Sort of backfired on them forty years later when they wanted Reagan to run for a third term though and Orrin Hatch suggested repealing the amendment. Needless to say, the Democrats laughed him out of the Senate chamber.
