But what does one call someone who endlessly repeats false information, after overwhelming evidence to the contrary has been presented? 

Donald Trump is a full-blown, unequivocal LIAR. His leadership of the "birther" movement alone earns him that label, which might as well be tattooed across his forehead. His serial lies about the ex-President's birthplace were debunked almost immediately, yet he willfully and continually repeated that false information, to his own benefit, for years. When, at the final moment of truth, he was asked to defend or refute his lies, he gave the wimpiest response possible, neither admitting to his lies nor defending his point.

With a history like that, how can any falsehood or half-truth he utters be considered anything but a lie?