I doubt Horner can maintain his position with such damning evidence against him. His behavior seems indefensible.
However, Horner is likely to play the corporate waiting game, e.g. let people forget or ignore the issue, especially given Max and Red Bull's success this season. He's been cleared by an the laughable internal investigation. Reports suggest he has the backing of Thai investors + all strategic partners, notably Ford, were left in the dark during the investigation and learned everything from the news.
He'll stay until major financial backers like Ford decide to pull out, and that doesn't seem likely anytime soon.