Snap awake = suddenly get awake? Ventilator = electrical fan? Air conditioner?
Context: The accident's power over him was diminishing, he said, as his ventilator sucked and hissed. He no longer snapped awake in the quiet hours, forced to confront, all over again, the fact that he had no sensation from the neck down. He didn't need to turn away when he was driven past the barn where he kept Buck, the thoroughbred horse from which he had been thrown in 1995, breaking his neck. But learning to live with his paralysis wasn't the same as resigning himself to it. "I've still never had a dream that I'm disabled," he said. "Never." He had vowed, controversially, to walk again by the age of 50. At the time, that deadline was three weeks away.
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Yes you have the correct meaning.
— Nona the brit
Yes you have the correct meaning.
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I think "at the time" in this case means at the time when he was interviewed for the article you are reading.
It is quite likely that by the time to article was published three weeks would have passed. Because of this nearness to the deadline, the author probably felt it would be important to clarify.
Also, I believe that Reeves was quoted as vowing to walk again by age fi