I found the solution the same day I post this but I forgot to share it. Sorry about that. Bytheway, I'm surprise nobody give an answer. Is there still something in this forum to help other guy ?
So, I think this is a problem of cookie and domain, or something like that.
I will use an example to explains it :
You have 3 shops : a.com which is the main shop, b.com, and c.com.
If you connect to a.com/adminXXXX/ you can see the live configurator from your main shop (a.com), BUT, it will not works with b.com and c.com.
The solution is to connect to the admin shop from the good domain.
For example, to see the live configurator of the B shop, you need to connect to b.com/adminXXXX/. Now if you open the "my shop" link, you will see the live configurator.
Do it for all of your shop.
Now, I will be able to connect from the main admin a.com/adminXXXX et it's still works.
That's why I thing this is a cookie which is assign to the domain, or something like that
Hope that help.