Persuasion is a particularly comforting read, because it's a book where good things happen, not in spite of the bad things or as consolation for the bad things, but often because of the bad things.
Anne loses her family home, and her family moves to a city she hates instead of staying in the familiar countryside like she wanted, but being forced outside her comfort zone is good for her. She's useful to her nephews, she strengthens her friendship with the Musgroves, she makes new friends with the Harvilles and Captain Benwick. It allows Captain Wentworth to come back into her life, and that seems like a bad thing at first, but it allows her to move past the regret of the past and into a new relationship.
Louisa's injury is a terrible turn of events, but it brings Louisa and Benwick together, and allows Anne to show her true worth in a way that makes Wentworth admit his love for her.
Even Anne's great regret, her refusal of Wentworth that led to eight years of misery, turns out to be a good thing. Wentworth's disappointment made him throw himself into his career, and his lack of a wife gave him freedom to go on voyages and into battles without worrying about how it would affect a family that relied on him. Anne's rejection--his first taste of failure--gave him enough maturity to keep the money that he made, and he came home a rich man who could well support a wife. Instead of starting out married life with stress and worry over uncertain funds, they are able to wed as people who are financially stable and secure in their love for each other.
It's a deeper, richer message than just saying that good things come to those who wait, or that someday you might get enough good things in life to make up for the bad stuff. It's saying that your suffering might be the necessary step to bringing about a life that's better than you could have hoped for. And that's very comforting.