After realizing what the Lowat tribe had done to Tair, Malak knew he had to do something. But he was at a loss—for several reasons. The most important one was naturally that he couldn't leave Sosora's side.
She needed him now more than ever. He was going to be there when she woke up. She would need someone to lean on, and Malak was going to be that someone.
Of course, he knew how much getting Tair back meant to Sosora. If Malak could have achieved that while she was unconscious or at least made good progress, he would have done it.
He wasn't doing it because he didn't know what to do. He couldn't exactly wander out of the forest and search blindly for any traces of Tair.
A member of the tribes shouldn't be able to hide well in any of the kingdoms. If he had the means and connections, finding Tair would be like finding a smoking ember in a pile of rocks.