From many interviews, we know that Stephenie Meyer loves Jacob (check out his "Character Analysis" in New Moon for details). So it's no wonder that, when it comes to naming his tragic flaw, she says,
Jacob doesn't have a tragic flaw. He has one goal and one hope. His goal is to save Bella's life. His hope is that he'll win her heart in the process. He fails at both. But that doesn't mean he regrets trying… Does he do everything right? Heck, no! But he's sixteen and he's making it up as he goes along. Those who are upset by some of his tactics should consider his youth and the fact that he is, after all, right. Bella is in love with him. (source)
Until the end, Jacob is convinced that he's the right choice for Bella:
"I'm exactly right for you. It would have been as easy as breathing. It would have been the natural path your life would have taken…" (26.207).
Even Edward agrees that Jacob is better suited for Bella, because he's strong enough to protect her and at the same time their relationship would allow Bella to stay human, to be with Charlie and Renée, and to have kids. "I even asked Alice if she could see that… [Bella] would be better off with you" (22.167), Edward says. But it's on Bella to decide and she seems to believe that fate inevitably ties her to Edward. The one thing that speaks to Bella's conviction that she's not meant to be with Jacob is that he didn't imprint on her.
Not that he doesn't try. In Chapter 8, when they walk along the beach and he first clues her in to the werewolf quirk of imprinting, he stares at her and then waves her off when she asks him what's wrong. The moment is subtle and easy to miss but, according to Stephenie Meyer, it was intended to show that imprinting isn't something you can force. So that kind of gets Bella off the hook and leaves Jacob with…what? Killing Bella before she's transformed into a vampire? A fight to the death against Edward? A lonely werewolf existence? The last option sounds unlikely because, as Stephenie Meyer mentioned, Jacob is not one to easily give up.
Throughout Eclipse, Jacob uses every weapon in his arsenal to convince Bella that he's the right choice for her. Although he tells Bella during their last conversation in Chapter 26 that "I won't cut you in half anymore," Bella suspects that he's just trying to prove to her that he loves her more for surrendering her to Edward. In fact, Jacob doesn't seem to have any intentions of surrendering her. He might not fight, but "he'll always be waiting in the wings" (26.253) – maybe even if Bella turns into a vampire (provided she doesn't stink too much).
We can also suspect that the reason he refuses to take his rightful position as head of the werewolf pack, as "Chief Jacob" as Bella puts it, is because he still hopes there's a chance to forego his werewolf life for a normal human life with Bella. Even if Jacob says that he knows that Edward really loves Bella and that Bella can't live without him, the epilogue – narrated by Jacob – seems to reveal that he's actually revolted by the idea of Bella's transformation and doesn't trust Edward to not kill her. At the same time, he's torn about whether he'd rather see Bella dead than a vampire: "Could I want to kill her? Could I not want to kill one of them?" (Epilogue.37).
His rage seems to be so uncontrollable that his only escape is to turn into wolf form. He disappears into the woods, "letting Jacob Black disappear" (Epilogue.83) behind him. But we're left to wonder for how long. What he is going to do? Will he interfere with Bella's transformation into a vampire? Will her transformation conjure up a war between vampires and werewolves? Will it come to a confrontation between Edward and Jacob, a fight to the death that they both admit "sounds like an intriguing idea" (22.140)? What are the chances that, faced with transformation, Bella will once again get cold feet and return to Jacob? Too many possibilities! The only option is to continue on to the last book in the series: Breaking Dawn.
For more info on Jacob and his claim to fame, check out his "Character Analysis" in New Moon.