I'm having trouble reproducing this behavior on your site. Using Chrome - I attempted to create a new user and was brought to the JomSocial registration page with an error that some fields needed to be filled out. I filled out these fields and then created a user. Then I logged out and attempted to log in again. I was logged in properly and brought to my profile page at /index.php/profile as expected.
Could you give more detailed steps on how you're producing that behavior? Specific URL, steps to take, etc.
I just logged in on your site. Been a while, but my credentials still worked. I was logged in immediately and normally.
Can you try from different browsers and/or let us know as many other details about how you're trying to login so that we can investigate further?