Actual sleep does take longer than it should.

But Dick does, eventually, drift off, despite the sheer volume of thoughts racing through his head and the impossible-to-ignore familiarity of Barbara tucked in beside him, close enough to hear her breathing, even when she's turned away from him. And as difficult as things have been, and how drastically different this is from anything he could have possibly expected to find himself in, it's that familiarity that gets him in the end. It's only when he's asleep that he curls toward her, not spreading out over that empty space between them but orienting toward her all the same, because that's what he always does.

No amount of banging on the door is going to wake him up either. As long as no one barges in he's staying very solidly unconscious, the only thing that would likely rouse him at this point is picking up on a high alert from her, and if all this place wants to do is spook them a little... well, it's not going to have much of an effect on him.

At least it won't be one of those 'sleeping for two days' situations. Maybe just a full night and then some.