There's a few moments before he actually falls asleep, where she can tell it's happening, and the rational side of her (with a tone much like her mother's) is telling her to shove him awake, so he can go to the couch.

But the less rational side (the side Percy always seems so capable of drawing out of her) is just content to continue watching him, with a soft smile on her face.

And then he's sleeping, before she can make up her mind. She shifts slightly, a test, but he doesn't budge; he's out like a light, and with the day he's had, she can't blame him. So Annabeth just finds herself curling up even further against him, allowing herself to get lost in his presence as she slowly drifts off, too.