Make sure to check you have placed the proper vbulletin license number in your config-inc.php file for vbulletin is the top choice here if it logs you out of
vb
Then check the cookie settings also in the database settings table settings 171-173. Make sure they are set like this
cookie path /
cookie prefix bb can verify this in config.php of vbulletin
cookie domain blank or .domain.com must match
vb