Recently we have been experiencing SBS 2011 Backup Failures on several servers relating to (VSS Microsoft Volume Shadow Copy Service). All of these servers are new installs and have no third party backup tools installed.
On a few occasions the issue was addressed by running PSCONFIG after the installation of Microsoft SharePoint Foundation 2010 Service Pack 1 (SP1) as outlined in the following article: http://social.technet.microsoft.com/Forums/en-US/smallbusinessserver/thread/94c5f178-f020-4d0f-ba7c-11c415d0d862/
However, on a number of other installations this update did not correct the issue. Research lead us to investigate the status of the ‘Volume Shadow Copy writers’ by running an elevated command prompt and typing vssadmin list writers. The output from this command identified a number of the writers were in:
State:  Waiting for completion
Last error: No error
Stopping and starting the Volume Shadow Copy service does not change the status. After reading many articles around this error we decided to do some testing of our own. A lot of the information we came across related to two SharePoint services:
SharePoint 2010 VSS Writer
SharePoint Foundation Search V4
What we found was that by stopping both these services and manually activating a backup it would complete successfully. However, the ‘SharePoint Foundation Search V4’ service will restart automatically. Therefore, once you have stopped this service you must initiate the SBS 2011 backup immediately.
Once the backup is completed successfully, we again ran vssadmin list writers in an elevated command prompt and all the VSS Writers reported as follows:
State:  Stable
Last error: No error
Once this condition was established for all VSS Writers we restarted the ‘SharePoint 2010 VSS Writer’ service and tested the backup several times more and again after a restart. The backups all completed successfully.
Hope you find this information helpful.
We have subsequently found that as soon as any further Sharepoint updates are applied the problem returns. The only way to constantly backup successfully again is to run PSCONFIG again.