That's normal.
You need really high peace and even then it doesn't last very long and can be instantly broken by the strong will of the Cu.
When I'm taming Cu these days and I have the peace skill on me, I'll use it for emergency relief. (as long as there's no one around that I can mess up with area peace)
I will lead tame a Cu and if it get too many bites in I will area peace to get it off me so I can heal up and try again.
Please note that if you are bleeding from one of their bites area peace will not get them off you. You have to wait until the bleeding stops then area peace.