If your child site is logging you out each time you refresh the page or navigate to any other page, try creating a user with the same username and password in the parent portal as the user you are using in the child portal.
The two users do not need to have matching security roles assigned. Once the user has been made, you can change the password in either one without breaking the fix.
This was an issue and a solution for me once in DNN 07.02.02. Mark Buelsing