Kili may have argued or lipped off, but he was so taken aback by Thorin's behavior that he was rendered speechless. It was no secret that Thorin could be a bit overbearing and harsh, but he'd never seen him this bad. Thorin didn't seem to care about them at all, his only focus was on the Arkenstone. 
Before Kili could begin to utter a response, Fili had quite literally stepped in for him. Big hearted as always, Fili spoke on his behalf and even offered to search in his place. Kili felt a twinge of guilt at that -- Fili must have been terribly tired too. They'd barely a moment's rest for days now.

Thorin grew dangerously quiet, his eyes flickering from Fili to Kili. Kili [i]did[/i] look exhausted. If he fell sick again, Oin would have to tend to him. They didn't have time for illness to get in the way of their search.
"Very well," he relented, if only for Kili to rest a little. "Kili, go rest. When you wake, I want you to help your brother."

Kili felt badly to bail on Fili, but he wasn't sure how much longer he could keep on his feet. The youngest felt a mixture of hurt anger towards Thorin, though he held his tongue and did not risk mouthing off to him. "I'll be back soon, Fili," he promised him quietly, then turned to leave the chamber, his eyes towards the ground.

Once he'd left the room, Kili breathed a small sigh of relief. Thorin was more than a little intimidating -- especially now. As he walked down the long, empty halls, Kili kept an eye out for Saeril, hopeful to find her. "Delva??" He called for her once, though not too loudly in fear his uncle should overhear.