It wouldn't surprise me if he thinks it's in his interest to keep the whole thing going right through the election. He knows the birthers are never going to vote for him anyway so he gains nothing by giving in, and keeping their deranged conspiracy theory in the headlines makes the republicans look a bit loony which could help push some independents into his camp.
It could be what he's doing, but isn't he the man who was going to be all about "change"? Instead of dopey political stunts, I thought "change" would be about honesty.
He also mentioned that his administration would be transparent. Apparently he did not mean it would apply to himself.