Ironically, though, Atticus does hope, and tells Tom's wife that there is a good chance that an appeals court will free Tom. However, by not giving Tom the same hope, Atticus may have inadvertently hastened Tom's death.
This occurred on the day when they took Tom to the prison camp. Tom's last words to Atticus were "Good-bye Mr. Finch, there ain't nothing you can do now, so there ain't no use tryin'" (ch 24). Tom had given up all hope in finding justice.
Atticus offered him no false assurances of making it right, because Atticus did not want to give him false hope.