Can’t login the site.

After enabling the plugin can not login to the site. I enter the username and password, but there is no reaction. The feeling that I did not enter the username and password. After going to any other page of the site I see that I have already entered. This is weird. After disabling the plugin everything works fine. But I like it and I would not like to replace it with something else. Please tell me how you can solve this problem?

The page I need help with: [log in to see the link]