The solution below will instruct you on how to enable and use the DBExclusion menu that is built-in to Veeam Backup & Replication v7 and greater.
Allow the writer service account access to the Volume Shadow Copy service via the registry:
On the VM you are backing up, open regedit.exe and navigate to: HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\VSS\VssAccessControl
If a DWORD value for the account assigned to the writer service is present in this key, it must be set to 1. In most cases, the relevant service account appears in services.msc as the log-on account for the service listed in KB2041. However, some writers have special accounts. For example, in MS SQL Server 2012 and later, if the DWORD value “NT SERVICE\SQLWriter” is present in the VssAccessControl key, it must be set to 1.
On next job run the specified database will be excluded from the Application-Aware Image Processing freeze task.
Note: If you are using a default or unnamed SQL instance (example: MSSQLSERVER) then only the server name (or IP address) should be added in the "Add Database" screen.