In reply to subtle:
I don't think the fundamental problem was that Claire was tired. As others have said, she's obviously very fit and, in that regard, would have been fine with a bit of extra food/drink/warmth. The problem was that her nerves were shot and she had completely lost confidence in her ability to negotiate the terrain.
I suspect her partner hadn't been up the route before. From the footage, it looks as though they were at the end of the traverse, below the Great Tower. If he'd done the route previously, he'd have known that, from the point of view of a second, by far the scariest part is over. From here on in, she'll have the rope running directly above her to the top of the Great Tower, with good hooks en route. Then an easy, if exposed, walk/crawl to the Gap, which she could have climbed down into with him belaying directly above her. He can then lead directly out so that, again, the rope is directly above her. And then it's pretty easy ground to the top. Additionally, the conditions looked pretty benign.
The traverse, on the other hand, if banked out will be very scary for those not used to trusting their feet on steep, loose snow - and you have to, as there doesn't tend to me much for the axes on the slabs to one's right! Add in the fact that gear is a little bit spaced, and it quickly becomes apparent to the second that they're going to take a big swing if they come off.