Symptom:
When running a backup, you receive the following message:

5/20/2013 1:43:48 PM :: Error: Client error: File does not exist. File: [E:\Backups\VMs\VM2013-05-20T010122.vib].
Failed to restore file from local backup. VFS link: [summary.xml]. Target file: [MemFs://Tar2Text]. CHMOD mask: [0].

Solution:
From what I gather, this error is generated when you do not have a full backup completed.  For example, lets say you have an external hard drive you backup to and your next scheduled backup is an incremental.  Now when your incremental backup runs, since a full backup does not exist, the incremental backup cannot be made and you result with the above error.

To allow your backup to complete successfully, you will need to manually create full backups for each of the "problem VMs", so the incremental can backup properly.  To do so, you can right click on your Veeam Backup Job and select "Active Full".  This will create a full backup and then let your scheduled incremental jobs run as intended.