Forum Cache login problem - ongoing!!! plz help!!!!
 

We have a problem related to authorization and sign out procedures on our copy of VBulletin forum. When the user authorizes (enters login and password) on the main page, the following happens: the user has to reload the page to see that he has authorized successfully. It also happens often that when the user is browsing the forum topics, he becomes logged out for some reason.
The logout problem is the same: after the user clicks Sign Out, the system indicates that the user has signed out successfully, but he stays logged on.

I must indicate that the forum is located on server in the wordpress folder which is the main system for the site. The structure of the forum and the site is the following

Forum is located in the folder that contains main website (wordpress)
The URL for the site and forum:
site: - mysite.com
forum: - forum.mysite.com
Forum version - 4.2.0, patch level 3.

The following has been done to resolve the problem:
1) The cookie domain was set - - .mysite.com
2) Cookie path - /
3) With the use of do_not_upload/tools.php all cache has been cleared, the tables that could be damaged were restored.
4) The forum has been moved to server root (/forum) and a subdomain was made.

All these actions didn't help. The only thing that worked was to launch forum on another server, where it is located separately from other sites and doesn't have the .htaccess file used in WordPress. So we have just moved the forum to another platform and everything worked.
But we really need to have the forum running properly on the original server.
Could you please suggest a solution to this issue, or a hint where the problem could be?