You can fix this issue by completing the following steps:
1. Login to FTP
2. Go to the root folder for your account (/)
3. Delete the file .my.cnf.
4. Then login to cPanel, and click 'MySQL Databases'.
5. Then click 'Home'
6. Then click 'Backup'
You will now be able to download your database backup successfully.
If you get further problems contact support, as this can be a server config problem too.