I had 5 Clans when I became Khan of Khans. Only 1 stayed with me. I'm not sure if it's working as intended, because I could also see from one standpoint that others would challenge your claim of being the Greatest Khan. The only clan that stayed loyal was the one I swore a blood oath with. If it's intentional, you think they'd add some flavor text about them resisting.
I actually don't mind them breaking away if you got a Subjugation CB on them/a war kicked off immediately...But right now, right now it's just mildly annoying.