There is an issue to login to the Adobe Connect using Custom Created Cookie

I'm Creating a Cookie using the parent domain (Ex: .adobe.com), then using this cookie i could be able to login to the Adobe Connect Server which is hosted in the same domain, this authentication and redirection part id done by separate application we needed to access Adobe Connect site using  Single Sign On (SSO) by clicking a link in our application, passing the adobe login screen.

Using Parent domain cookie could able to login but after hit log out in adobe connect we could not log to adobe connect server with out signing. it redirects to the Adobe Connect Login Screen.

the issue is after logout Adobe Connect Rejects the Parent domain cookie. is there a way to sort out this issue ?