Once the quest to kill Paarthurnax has been started, he can be killed at just about any time. I believe you can do so once you've read the Elder Scroll, though I may be wrong as I really don't feel the urge to kill Paarthurnax and get some stupid Blades followers to make dragon fights even more nerfed.
cmp007, it sounds like you've got a glitch. Reload your last save and try again. You may also want to try dealing massive amounts of damage all at once, either with expert destruction spells, enchanted and upgraded daedric weapons, or with werewolf power attacks.
Also, Paarthurnax can be killed after the main quest. He is not supposed to become essential. This is a glitch.
I would actually gander that Paarthurnax is never marked as essential or made invincible. I haven't tested this whatsoever, though. With how helpful and wonderful his character is, I'm sure very few people ever actually seriously attack him before getting the quest to kill him.