Going by clues dropped in the franchise, The Klingon/Federation border didn't always have a neutral zone.
TOS always mentioned the Klingon border. The mention of a neutral zone did not appear until the movies. by the time of TNG, the Klingon border has become just a border again.
I get the feeling that the Federation/Klingon neutral zone only existed for a short time anyway. Maybe 20ish years.