The question raised in the title of this post is fairly naive. He was in the middle of a Pakistani military city. They knew, and they don't mind if you figure it out. It won't be acknowledged in the media. Since they're mostly corporate-owned, no one will ask the question in any meaningful way.
Well, if you were the President, would you have killed Bin Laden in the middle of the revolutions in the Middle East? Wouldn't have been very good timing. Might have hit the reset button on all that. Much better to let it run its course. Bin Laden wasn't going anywhere. Not with the Pakistanis having him so well controlled.
When did the President need the rhetorical high ground to win the war with the Republicans? Who did he fear more, Bin Laden, who was cornered, and controlled by a US ally, Pakistan, or Mitch McConnell, Eric Cantor and the Koch brothers? Again, we don't have a choice but to take things at face-value. Obviously the Republicans were doing a lot more damage to the US than Bin Laden was. A good President picks his battles and fights them on his own terms. Could the President use Bin Laden to win the war with teh Republicans? Well, duh. (Hello.)
And it's working. The Republicans are retreating on all fronts. (But that's probably all theater too, the real war is much more complicated than the battle between two political parties that report to the same multi-national corporate bosses.)
Bin Laden knew it was over for a long long time. According to reports he didn't leave the compound for five years. He probably couldn't get out if he wanted to. He didn't have Internet or phone service. His only connection to the rest of the world was through a courier, and we knew all about that. Did Bin Laden know we knew? I think so. And there was nothing he could do about it. The man was cornered. And he was that way for a long time.
Using an Occam's Razor approach, the deal he had with the Pakistanis and the US probably went something like this. As long as there are no major acts of terrorism in the west, and as long as we don't need you to die for some greater political purpose, you get to live. But you have to stay confined to this prison, with one wife and a few kids, a vegetable garden and reefer. Bin Laden's life was a chip that could be cashed in for political gain when needed. On Monday the clock ran out for him.