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.
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I believe this is working as intended - while there are reports of being able to defeat Paarthurnax after having completed the main quest, according to the Prima guide, and in my own experience, completing the main quest causes him to be flagged as essential (and thus unkillable).
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.