I completed the main quest line, and now have to kill paarthurnax for the blades. He's on the usual wall, I can talk to him, but his health won't fall below zero, as if he's still a quest character. Why won't he die? I'm playing on an Xbox 360.
I've also seen reports that this status is temporary and if you stay away from the Throat of The World and advance the in-game calendar by several months, (I.E. by waiting), he will reset and become killable again. YMMV.