I just tried to register on the site, and I'm getting a Fatal error from our Kunena Profile plugin. Is that enabled? If so, is Kunena installed? If not, please disable that plugin.
That's not the cause of the problem you're having though. Facebook uses Javascript to set a cookie in the user's browser to identify them. It seems that there's a bug in Facebook, introduced in the last few days, where the cookie is not properly destroyed when the user logs out. We're waiting to get a response from Facebook on the issue.
In the meantime, to the 2 other user's who have reported a similar issue, we've recommended checking your Facebook Application settings. Make sure the Site URL and Domain look are set as follows:
Site URL:
tickerpickerpro.com/ (or
tickerpickerpro.com/joomlatest/)
Domain: tickerpickerpro.com
If those settings are incorrect, then Facebook may not be able to delete the cookie properly, and that would be the cause of the problem.
Alternatively, in the meantime, you can also disable the automatic login function, though I understand that may not be how you want your site to operate.
Hope that helps,
Alex