First of all make sure that client and domain's administrator have corresponding permissions.
I've ticked every box on both the client permissions and the domain administrator access screens.
In the documentation it says -
To back up a database:
1. Go to Domains > domain name > Databases.
2. Select a check box corresponding to the database you want to back up and click Back Up. [
THE "BACK UP BUTTON DOES NOT EXIST]
3. Specify the name of the backup file and click OK.
4. If you want to download the resulting backup file, click the file name on the next page after the backup process was finished. Specify the location where you want to save the file and click Save.
5. Click OK.
To back up all databases on a domain:
1. Go to Domains > domain name > Backup Manager > Database Backup Repository, make sure that All domain repositories is selected in the Database field, and click Back Up. [
THE "BACK UP" BUTTON EXISTS BUT IS GREYED OUT]
2. Specify the name of the backup file and click OK.
3. If you want to download the resulting backup file, click the file name on the next page after the backup process was finished. Specify the location where you want to save the file and click Save.
4. Click OK.