TLDR
Restart the Microsoft Exchange Replication service, either via services.msc GUI, or via:
net stop MSExchangeRepl net start MSExchangeRepl
Recently I was asked to look into why somebody was having the following error during Agent level backups of an Exchange 2013 server:
The job failed with the following error: The database specified for the snapshot was not backed up because the database was not mounted.
Once this had happened, all subsequent Exchange server backups would fail as well. They had always been resolving it with reboots of the Exchange server, based on an article they had found on Veritas, but this always meant a 10-15 minute outage, which they were trying to avoid – they are a small outfit with a single Exchange server.
Reading through the Veritas documentation, the database backups ran through the Microsoft supplied VSS writers, and it looks like the VSS process was getting stuck, and hanging. The VSS for Exchange in Exchange 2013 onwards is part of the Microsoft Exchange Replication service. Restarting this service resolved the failed backups.
I suspect the reason why it is hanging is their Exchange server is virtualised, and their hypervisor’s disk system isn’t really fast enough, with occasional spikes in latency.