Answer:
I think President Jefferson did not run for third term because, during his second term, in his attempt to leave the U.S out of the Napoleonic Wars, he implemented the Embargo of 1807 because France and Britain, who were in the war, were harassing the U.S merchant ships.
The embargo closed the U.S ports to foreign trade and it hurt the american economy. The embargo was wildlly unpopular and the U.S still went to war against Britain in 1812.
I hope this help you!:)