First, go to Start > Control Panel > System and Security > Windows Firewall > Allow a program through Windows Firewall and check the box next to HamSphere. If you can't find the application in the Allowed programs and features window, press the Allow another program button, navigate to the installation directory, select the executable file and press Add.
After that, from the Advanced Settings select Inbound Rules > New Rule. Check the Port box, click Next, select All local Ports and follow the self-explained steps. Also, make sure that your security program doesn't block the connection.
If it still doesn't work, it is possible that the HamSphere servers to be temporarily down or under maintenance. Also, check if you entered a wrong password using the Lost Password? form provided by the developers. If none of these helped, I suggest you download and install the latest version of the software.