If CompleteFTP detects an invalid or missing license, it goes into restricted mode. In this mode it only permits local connections (i.e. connections originating from the same machine it is installed on).
This problem is generally because of a migration to a new machine. It is also possible if CompleteFTP is running in a virtual machine that the machine's ID has been changed. In both these scenarios the machine ID encoded in the license does not match that of the new machine.
The resolution is to activate the installation. This necessarily uses up one of your purchased licenses. If you are moving your CompleteFTP installation, you can contact support to request an additional license be allocated.