There are multiple causes for this failure to connect, the following is a list of the most common causes:
1. The server where the console is installed cannot reach the Veeam Backup & Replication server due to network limitation.
2. The server where the console is installed cannot resolve the hostname or FQDN of the Veeam Backup & Replication server entered.
3. A firewall is preventing communication between the server where the console is being run and the Veeam Backup & Replication server.
4. On the Veeam Backup & Replication server the Veeam Backup Service is not running.
5. If this is a recent installation and you have never been able to launch the console, it is likely that the Console software has been installed but not the Backup & Replication software itself. To correct this, uninstall the software through Programs & Features. Then, launch the Setup once more. Make sure you click the large Install button to the left rather than any of the install buttons on the right. This will install the Backup & Replication software as well as the console software. For reference, the red square below:
There may be other causes, please contact Veeam Technical Support if you find a cause not listed.