Strato does not support all necessary PHP-functions in all hosting packages.
So we noticed that the ZIPArchive-Support was missing in a basic-hosting package, which comes with PHP 5.2.17. We got the information, that the ZIPArchive-support, which is necessary for the backend-backup-functionality, is only supported in the PowerL-hosting package, which will cost 11€/month more.
Plugins also have problems, couldn't write fresh user-xml-files (multi-user-plugin) or googlemap-settings. So I think it is again the problem with FTP-User and main user permission.