Bekah Evie Bel suggests The Wishsong of Shannara by Terry Brooks (1985) in the comments:
Puts me in mind of Wishsong of Shannara. Weapons Master Garret Jax who is and never will be defeated but dies saving the protagonist, a teen boy with elven blood. They travel through various lands and there are creatures from Faerie, kind of - the Jachyra that kills Allanon and Garret. One of the places the boy goes to is kind of Faerie like, the place protecting the Ildatch. And of course the King of the Silver River is the last of the Faerie and certainly he and his land are integral to the story. But the cover description doesn't match. – Bekah Evie Bel Dec 4 '15 at 21:49
Here are some quotes about Jax from the book:
His description as the "Weapons Master":
Even in a tiny Southland village like Shady Vale, they had heard of Garet Jax. He was the man they called the Weapons Master—a man whose skill in single combat was so finely developed that it was said he had no equal. Choose whatever weapon you might or choose no other weapon than hands, feet, and body, and he was better than any man alive. Some said more than that—he was the best who had ever lived. The stories were legend. Told in taverns when the drinks were passed about in the hours after work was finished, in village inns by travelers come from far, or about campfires and hearths when the night settled down about those gathered and the dark formed a bond that seemed strengthened somehow by the sharing of words, the stories of Garet Jax were always there. No one knew where he had come from; that part of his life was shrouded in speculation and rumor. But everyone knew at least one place that he had been and had a story to go with it. Most of the stories were true, verified by more than one who had been witness to its happening. Several were common knowledge, told and retold the length and breadth of the Southland and parts of the other lands as well. Jair Ohmsford knew them all by heart.
In the midst of the shadows and the half-light lay Garet Jax. Stunned, Jair and Slanter came forward. The Weapons Master lay back against a gathering of rocks, his black-clad form torn and bloodied, the slender sword still gripped in one hand. His eyes were closed, as if he slept. Hesitating, Slanter knelt beside him. “Is he dead?” Jair whispered, barely able to make himself speak the words. The Gnome bent close for a moment, then drew back again. Slowly, he nodded. “Yes, boy—he’s dead. He finally found something that could kill him—something that was as good as he was.” There was grudging disbelief in his voice. “He looked hard enough and long enough to find it, didn’t he?” Jair did not answer. He was thinking of the times the Weapons Master had saved his life, rescuing him when no one else could. Garet Jax, his protector. He would have cried if he had been able, but there were no tears left to shed. Slanter came to his feet and stood looking down at the still form. “Always wondered what it would be that would finally kill him,” the Gnome muttered. “Had to be something made of the dark magic, I guess. Couldn’t be anything made of this world. Not with him.” He turned and glanced about apprehensively. “Wonder what’s become of the red thing?” Tremors shook the mountain, and the rumbling rolled out of the valley. Jair barely heard it. “He destroyed it, Slanter. Garet Jax destroyed it. And when the Ildatch was shattered, the dark magic took it back.”
You might be thinking of this line, about the flaw being caring about something, also it doesn't relate to Jax:
“Someone asked all of us to come,” Helt pointed out. “We didn’t have to come, though; we chose to come. It’s no different with the Gnome. He chose to come with you to Culhaven—probably he wanted to come. It may be that he wants to come now, but can’t admit it to himself. Maybe he’s even a little frightened by the idea.” Jair frowned. “Why would he be frightened of that?” “Because it means he cares about you. There isn’t any other reason that I can think of that he would be here.” “I hadn’t thought of that. I guess that I thought just the opposite from what he’s been saying—that he didn’t care about anything.” Helt shook his head. “No, he cares, I think. And that frightens him, too. Trackers can’t afford to care about anyone—not if they expect to stay alive.” Jair stared at the Borderman a moment. “You seem pretty sure about all this.” The big man rose. “I am. You see, I was once a tracker, too.”
As for the cover, I have a feeling that you might be conflating it with the cover of The Sword of Shannara, another book in the series:
...which shows a half-sunken sword and a small creature with an outstretched hand.
It's a long shot, but might this be possible?