Hi Advait Mohammad,
First, I don't think you have to reboot the server, because SqlServerWriter is hosted by the SQL Server VSS Writer (SQLWriter) service, restart that service from an elevated Command Prompt:
net stop SQLWriter
net start SQLWriter
Microsoft specifically recommends restarting the service that hosts a failed VSS writer when the writer continues returning errors, and restarting SQLWriter does not restart the SQL Server Database Engine.
Afterward, run vssadmin list writers and confirm that SqlServerWriter reports State: [1] Stable and Last error: No error before retrying the VM backup. If it fails again, check Event Viewer > Windows Logs > Application for VSS/SQLWriter errors and review C:\Program Files\Microsoft SQL Server\90\Shared\SqlWriterLogger.txt
For additional details, see Microsoft's SQL Server SQL writer documentation and the VSS Writer Errors and Vetoes documentation.