I was on a flight back from AMS a few months ago, and the CC were debating whether to throw a guy off or not. He was walking OK, but had eyes like saucers and admitted to CC when questioned that he "hadn't slept for two days".

The CC had a back and forth about it, and eventually let him stay. Although I'm fairly sure he was only allowed to stay as he had hold baggage and unloading it would have delayed the flight.