When Silas and Timothy arrived from Macedonia, Paul was occupied with the word, testifying to the Jews that the Christ was Jesus.  And when they opposed and reviled him, he shook out his garments and said to them, “Your blood be on your own heads! I am innocent. From now on I will go to the Gentiles.”  And he left there and went to the house of a man named Titius Justus, a worshiper of God. His house was next door to the synagogue.
It is wrong to suppose that we never give up on people. In one sense it is very true. We should never stop praying for any lost person we know to come to faith in Christ. But that does not mean that we never give up working with them. Paul knew that he would be wasting his time in Corinth continuing to try to evangelize the Jews there who were refusing to accept the Gospel. So he went to others. We are not all itinerant evangelists who have the option of leaving a people group to spend time with another, but we should use wisdom to know when it is time to spend time in more productive fields. It is not a denial of the power of the Gospel to work where the people are more receptive. Let us pray for wisdom to know when God is saying “persevere” (as He did to Paul later in the same city) and when He is saying “leave this place” (as He seemed to have done with Paul in this instance).