Below is a list of causes and solutions organized from most to least common:
The Veeam Backup Service has not started yet.
The Veeam Backup Service is set with the startup type "Automatic (Delayed Start)," this means that when the OS has just booted, it may take up to 3-5 minutes before the service starts.
The Veeam Backup Service is unable to start.
If you find that the Veeam Backup Service on the Veeam Backup Server is not started, start it. If it fails to start, create a support case and include the file: C:\ProgramData\Veeam\Backup\Svc.VeeamBackup.log from the Veeam Backup Server.
Note: The log file mentioned contains information about the Veeam Backup Service. If the service fails to start, there will be information about why the service was unable to start.
If the hostname of the Veeam Backup Server was changed just prior to this issue occuring, review KB2350.
The Console is unable to reach the Veeam Backup Service due to a network limitation.
When running the Console on a machine other than the Veeam Backup Server, that machine must be able to reach the Veeam Backup Service on port 9392. First, verify that the Veeam Backup Service is running on the Veeam Backup Server, and then test connectivity to that service from the remote machine using the following PowerShell cmdlet:
(Replace <hostname/ip> with the hostname or IP of the Veeam Backup Server)
The server specified in the Console connect window is incorrect.
This can occur in environments where the Veeam Backup & Replication Console is installed on a different machine than the Veeam Backup Server, and the Veeam Backup Servers hostname or IP has recently changed. Check connection settings and ensure the correct server has been specified.
(New Deployments Only) The Veeam Backup & Replication software has not been installed.
In rare cases, a mistake during deployment may have occurred where only the Veeam Backup & Replication Console was installed. In this situation, there will be no Veeam Backup Service on the machine. This can also be identified by attempting to run the Veeam Backup & Replication installer on the Veeam Backup Server and observing the message "Please uninstall console first." on the entry for installing Veeam Backup & Replication.