You know what, I've got an idea that might put this issue to rest (well, for most people, anyway).
I propose that, if enough people really believe President Obama was not born in Hawaii, they make him an offer. It could be a large number of people organizing and collecting money, or just a few wealthy opponents (or seekers of truth) putting up some of their own money. Get together about $5 Million and make a very public announcement to this effect:
President Obama, if you will make a request of the Hawaii DOH to issue another certification of live birth, such that we can see that it came directly from them, then we will donate $5 Million to the Kids Dying from Malaria foundation. Sure, Mr Obama, you don't want to legitimize these 'birthers' by proving again (in his mind) that you were born in Hawaii. But, are you really going to let the malaria kids die? All you have to do is indulge this nonsense (again, in his mind) one more time and think of the lives you can save?
As it is, there's no reason for President Obama to demonstrate anything further. I don't think this situation hurts him in the least politically. So, his failure to do more to demonstrate that Hawaii is indeed his birthplace isn't probative with regard to whether or not it is. Even if it is his birthplace, it makes sense - on some level - for him to just ignore this matter. However, if you create a good reason for him not to (e.g. the criticism he might get from some portion of the population for turning down a significant donation to a worthwhile cause), then his continuing to ignore the issue might be somewhat probative. I suspect he'd realize he was in a bit of a box and tell the Hawaii DOH to release another certification.
And, the money would go to something good. Win/win.