The Doctor only stirs some time through sleeping because the TARDIS hums through his consciousness, delighted and rested, much the same as himself.

Except when he tries to move to check on her, he can't. Which is very weird, because this isn't supposed to be a problem for him. Is never a problem for him, so why? Did something break aboard his ship while her defenses were down? Was he captured? Did he need to launch a rescue mission for him and Martha--

Martha.

Feeling a bit foolish, he supposes his ship wouldn't seem so happy if there were intruders boarding her.

He remembers that there's another body in his bed, and realizes that some of the fault in the entanglement is on him, just as much as Martha. He also realizes that he's awfully comfortable, and doesn't really want to deal with the awkwardness of pulling apart yet.

Besides, humans need more sleep than Time Lords. He's just doing Martha a favor. It'd be rude to wake her up so early in her sleep cycle.

So he doesn't move and goes back to sleep. It's the right thing to do, after all.