Is there a character who has not given up on something no matter what the outcome will be in To Kill a Mockingbird?

Atticus Finch is a character who perseveres in his defense of Tom Robinson despite the cultural climate of Maycomb and the negativity against him because he feels he must do so, no matter what the outcome will be.

When he is asked to defend Tom Robinson in the case brought against him by the Ewells, Atticus feels that he must accept this case because it "goes to the essence of a man's conscience." When asked about this case by Scout, he tells her that he could not go to church and not feel like a hypocrite if he does not try to help Robinson.

Before the trial begins, Atticus has great pressure put upon him to change the venue of the trial as the influential men of Maycomb come to his front lawn on a Sunday afternoon. Then, while Tom is held in the jail, a drunken, angry lynch mob drives up, demanding that Tom be handed over to them. But, a stalwart Atticus Finch, who has been sitting before the jailhouse door under the light, stands up to them and their dangerous threats. 

Despite the insults that are even hurled at his children by relatives and neighbors and others, Atticus pursues every path to justice for Tom Robinson, feeling a duty to do so. His cross-examinations of Bob and Mayella Ewell are polite, but thorough and legally brilliant as he incisively brings out the truth from Tom's accusers. Indeed, they leave no doubt in any rational man's mind that Tom is innocent. Furthermore, Tom's testimony underscores the vindictiveness and absurdity of the charge against him.

Nevertheless, like Mrs. Dubose, Atticus knows that he is beaten before he has begun. Still, he never stops trying as he makes a brilliant and cogent closing statement which appeals to the reason and the Christian values of the twelve men: 

"I am confident that you gentlemen will review without passion the evidence you have heard, come to a decision, and restore this defendant to his family. In the name of God, do your duty."

After the tragic end to this trial, Miss Maudie pays tribute to Atticus, who with personal integrity and Christian conscience has made every effort to convince people that justice should perceive no color or social class, by saying, "We trust him to do right."