Issue: SBS 2011 backup failed with the following error:
Backup unsuccessful
A Volume Shadow Copy Service operation failed.
Unknown error (0x800423f0)
This error occurs after the installation of the update Sharepoint 2010 SP1.
Resolution: (Taken from TechNet.com)
1. Open an Administrative command prompt.
2. Change directory to C:Program FilesCommon FilesMicrosoft SharedWeb Server Extensions14BIN
3. Run PSConfig.exe -cmd upgrade -inplace b2b -force -cmd applicationcontent -install -cmd installfeatures
Link: TechNet.com