If you despair of something, you feel that there is no hope that it will happen or improve. If you despair of someone, you feel that there is no hope that they will improve.
1. arising from or marked by despair or loss of hope;
"a despairing view of the world situation""the last despairing plea of the condemned criminal""a desperate cry for help""helpless and desperate--as if at the end of his tether""her desperate screams"