Ryuutaro was glad once Hayato fell asleep. Now he was at peace at least...
He himself was feeling exhaustion finally making itself noticeable, but he didn't want to give in to it. Hayato was injured... If he slept now... Who could guarantee that Hayato would still be here, still be alive, when he woke up?
And they weren't safe at this place either...

So, as tired as he was from all the emotional pain, Ryuutaro fought sleep with all he had, not willing to surrender.