Jo has said that the fact that Dumbledore didn't try to kill Voldemort in the duel in the ministry at the end of the 5th, IS really important. Yet again, a Jo clue that is 'really important'!! Ta Jo for the heads up However, if it is 'really important', why? What's Dumby saving Voldemort for?
Is it just that he doesn't want to deny Harry his vengence? That sounds particularly morbid for Dumbledore. It can't be about the prophecy because Dumbledore made it clear that that shouldn't/can't decide anyones' actions. So how about, Voldy is still Tom Riddle and Dumby has taken an oath to protect Hogger's students no matter what, forever??

About the "he doesn't have long for the world anyway...' line, i don't think there is anything profound in killers being able to sense the imminent death of people/prey.