Thank you for posting! Downloading it the way you've been attempting is the best way to backup your database from Managed WordPress. If you're still having trouble doing it that way, reach out to our support team to troubleshoot further.
Heather - GoDaddy | Community Moderator 24/7 support available at x.co/247support
Although is not possible to do a full backup (files and databases) to a single Zip file, it is possible to download the files and database separately. You can download a copy of the files to your local computer using an FTP client and you can export a copy of the database using phpMyAdmin.
KristyW - GoDaddy | Community Moderator | 24/7 support available at x.co/247support | Remember to choose a solution and give kudos.