freitasm: A good point. If you are not hosting anything then CGNAT shouldn't be a problem as there is no incoming connection.
Yes, CGN platform's generally come with default settings on session timeouts and these sometimes need to be tuned for specific services. PSN is one of these services that requires tuning as (wouldn't it be nice if PSN actually supported IPv6 **sigh**) it has a 10 minute keep alive when idle. If the CGN platform is tuned so that sessions on the ports that PSN uses have a timeout larger that 10 minutes then the log out issue goes away.