While the third book will hopefully shed even more light on this, we get an explanation from Bast at the end of The Name of the Wind. Essentially, Kvothe is so weak because he's been playing the role of an Innkeeper for so long, he's forgotten that it was a role, and therefore it is becoming reality.
“It’s like ... have you ever heard the story of Martin Maskmaker?”
Chronicler shook his head and Bast gave a frustrated sigh. “How about
plays? Have you seen The Ghost and the Goosegirl or The Ha’penny
Chronicler frowned. “Is that the one where the king sells his
crown to an orphan boy?”
Bast nodded. “And the boy becomes a better king than the original. The goosegirl dresses like a countess and everyone is stunned by her grace and charm.” He hesitated, struggling
to find the words he wanted. “You see, there’s a fundamental
connection between seeming and being. Every Fae child knows this, but
you mortals never seem to see. We understand how dangerous a mask can
be. We all become what we pretend to be.”
Chronicler relaxed a bit,
sensing familiar ground. “That’s basic psychology. You dress a beggar in fine clothes, people treat him like a noble, and he lives up to their expectations.”
“That’s only the smallest piece of it,” Bast said. “The truth is deeper than that. It’s ...” Bast floundered for a moment. “It’s like everyone tells a story about themselves inside
their own head. Always. All the time. That story makes you what you
are. We build ourselves out of that story.”
Frowning, Chronicler opened his mouth, but Bast held up a hand to stop him. “No, listen.
I’ve got it now. You meet a girl: shy, unassuming. If you tell her
she’s beautiful, she’ll think you’re sweet, but she won’t believe you.
She knows that beauty lies in your beholding.” Bast gave a grudging
shrug. “And sometimes that’s enough.”
His eyes brightened. “But there’s a better way. You show her she is beautiful. You make mirrors of your eyes, prayers of your hands against her body. It is hard, very
hard, but when she truly believes you ...” Bast gestured excitedly.
“Suddenly the story she tells herself in her own head changes. She
transforms. She isn’t seen as beautiful. She is beautiful, seen.”
“What the hell is that supposed to mean?” Chronicler snapped. “You’re
just spouting nonsense now.”
“I’m spouting too much sense for you to understand,” Bast said testily. “But you’re close enough to see my point. Think of what he said today. People saw him as a hero, and he
played the part. He wore it like a mask but eventually he believed it.
It became the truth. But now ...” he trailed off.
“Now people see him as an innkeeper,” Chronicler said.
“No,” Bast said softly. “People saw him as an innkeeper a year ago. He took off the mask when they walked out the door. Now he sees himself as an innkeeper, and a failed
innkeeper at that. You saw what he was like when Cob and the rest came
in tonight. You saw that thin shadow of a man behind the bar tonight.
It used to be an act....”
This last part is speculation on my part, but I believe that Bast's explanation may relate to the concept of Alar, as used to create sympathetic bindings.
When using sympathy, an arcanist splits off a part of his mind to contain the utter belief in the binding. The stronger the belief that the binding works, the stronger the binding. It is repeatedly mentioned how unusually strong Kvothe's ability with his Alar is, and how effortless he makes complex applications of Alar seem.
If Bast's explanation that Kvothe's change in self-perception is responsible for Kote being "a thin shadow of a man" is correct, it seems reasonable that Kvothe's particular talents for using his belief to manipulate reality may be working against him, making this more of a dramatic and fundamental change than it might be for a lesser man.