This is despite all the servers hosting SQL databases having jobs which have been completing successfully every night since we installed Veeam.
It might be this issue: https://www.veeam.com/kb2788
The error message is "Failed to export database: database name The system cannot find the path specified"
I'm of the view that this is permissions related, if anyone can advise on which particular permission should be granted and where to do it that would be much appreciated.
It's a little shocking however that Veeam has been reporting backup of all SQL servers as 100% successful when the SQL databases were never restorable. Agreed, I should accept responsibility as well, I assumed that seeing the files available for restoration and never seeing any failed backups meant the files would be restorable. You can't restore these files using any method such as restoring to another server or restoring the flat files. They're listed as available just like anything else.
Luckily a DBA who left the organization more than 6 months ago had a pretty good backup system in place so I was able to recover the files after unpicking the details of his alternative backup.
I don't think Veeam Backup & Replication should report these servers as successfully backed up and list all the databases available in restorations when they aren't.