When doing a backup on a new server where I restored Plesk domains from an old server, I tried to do my first manual backup via the Plesk 8.6 control panel. I receieved the error message:
Invalid syntax on line 1.

I also tried doing a backup from the command prompt with the command:
domain_bu --backup --domain-name=CompanionSoftware.com --dump-file=C:\Temp\BackupCompanionSoftware.com.bak
Once again, I got the error message:
Backup process has failed for domain 'CompanionSoftware.com'
Invalid syntax on line 1.
I couldn't find any help for this problem on Google or the Plesk support knowledgebase. However, I appear to have stumbled upon the problem and a solution. In the folder:
C:\Program Files\Parallels\Plesk\Backup
I found a 0-byte file named "certificate". Since a 0-byte file contains no information (other than its existence), it seemed rather odd. So I deleted it on the assumption that perhaps it couldn't be overwritten or at least it wasn't of any use. After deleting the 0-byte certificate file, my backups are working again!