How can I fix "Cannot perform a differential backup ... a current database backup doesn't exist"?
If something is taking a snapshot behind the scenes that breaks SQL differential backups causing a full to need to be taken before a new differential.  You can either stop whatever is taking the snapshot or ensure you're taking a full backup afterwards before you try to do a differential.  If you use Ola Hallengren's Maintenance Solution that can automatically change a diff to a full when it runs into this scenario.