I ran into this issue, where after sometime the SMS Build-in backup function would fail.
When running the SMS_SITE_BACKUP from Window Services (services.msc) it would fail with some of the following errors:

SMS_SITE_BACKUP failed. Please see previous errors.

Error: SMS Writer service either does not exist or is not running .

Error: GatherWriterMetadata failed.

SMS_SITE_BACKUP failed. Please see previous errors.

STATMSG: ID=5060 SEV=E LEV=M SOURCE=”SMS Server” COMP=”SMS_SITE_BACKUP” SYS=Server001.domain.com SITE=PS1 PID=67372 TID=61212 GMTDATE=Thu Dec 10 01:20:41.530 2020 ISTR0=”Error: GatherWriterMetadata failed.” ISTR1=”” ISTR2=”” ISTR3=”” ISTR4=”” ISTR5=”” ISTR6=”” ISTR7=”” ISTR8=”” ISTR9=”” NUMATTRS

Resolution:
List the VSS writers available with the following command: VSSADMIN list writers
If you find the SMS Writer to be missing run the following commands:

Net stop SMS_SITE_VSS_WRITER
Net start SMS_SITE_VSS_WRITER

This should add it back to the list as shown below. Now restart you SMS_SITE_BACKUP (can be done form services.msc) and review the logfile: smsbkup.log. it should now be running.

The issue here was caused by another backup solution using the Volume Shadow Copy Service (VSS). So fixing also required the other solution to be removed/reconfigured.