Obama beat Romney in the third debate, but it may not have made much difference. His initial failed performance allowed the Romney campaign to rapidly gain momentum that Obama has not be able to recover fully from.
Opponents have the inherent advantage at this high level. They share the stage with the President and are thus allowed to be seen on equal footing. Therefore, it’s the incumbent’s to lose.
It cannot have hurt that Obama performed well in the 2nd and 3rd debates, but it did not help him as much as it would’ve had he done well in the first.