You probably need to set up your Session cookie configuration to allow a session id established by one web app to be shared by another. By default, the Session cookie path is that of the context path of the related webapppage. So, if you have web app A at /A and web app B at /B, a session id established by /A would not be able to be used by /B, making single sign-on impossible.
So, you need to configure a path that is valid for all the webapps that wish to share the session. In the example above, the only common path is "/". However, if you have 2 webapps, one at "/one" and the other at "/one/two", you could configure the common path as "/one".
Check the wiki page Session Configuration for information on how to configure Session cookies.