OK, *this* is an important point. Characters in #TheLordOfTheRings are constantly "despairing", but to despair is not necessarily to give up.
In the story we see *three* reactions to despair. Frodo, Faramir - in fact, most of the principle cast - each feel a sense of hopelessness at some point, but continue to push forward. Some characters are overwhelmed and do nothing - this is Theoden, when we first meet him. And some actively subvert the heroes - see Denethor and Saruman.