Sometimes a VSS writer stops working and this can usually be seen in the logs of a failed backup job.

You can check which VSS writer is in a failed state by running the command vssadmin list writers

To fix this, you can either reboot the machine, or try to restart the corresponding service. However, the name of the VSS writer does not always match the name of the service you need to restart. For example, the if the VSS System Writer has failed, you need to restart the Cryptographic Services service.

Microsoft published a description of many VSS writers on this MSDN page:

The full list of writers and corresponding services compiled by Ansgar here is also extensive and kept up-to-date:

See also the notes from Datto and Arcserve.