The client can not connect to Magento 1.9.2.4

The customer visits the website and can log in, but when he logs out, he can not log in anymore. When they click to connect, the login page refreshes.

In addition, if I delete the site cache with the help of our Supercacher utility located in our Siteground control panel, the client can then log in again, but if it disconnects itself, he can not connect anymore.