I can’t see this as anything to do with the forum. Do not forget that your users do NOT log into the forum – they log into the website. This is all to do with the core WordPress procedures. When a forum page is requested – it is the WP core that informs plugins like SP on whether the user is logged in or not.

So you really need to assess what is happening to your core login process. So if, for example, you are using some sort of membership plugin, do you have it set up correctly. Also remember that WP uses cookies to determine a users status when requesting a page.