God did not give-up with Jonah. He still wanted Jonah to fulfill God’s original plan, purpose or burden that God called him for.
In Jonah 3 it says that God spoke again to Jonah. God speaks again. God again asked Jonah to go to Nineveh, the city He had originally commissioned him to go to. Eventually Jonah obeys, goes to that city and preaches, and as a result those people turned away from their unrighteousness and to God. See more at: Jonah in the Bible