Dropmysite will backup all the files and folders that you indicated that you wanted backed up. To see the directories that you have indicated that you want backed up refer to ‘How to: Exclude Directories from your Backup’ and ‘How to: Exclude Specific Files and Folders from your Scheduled Backup.
If you still see some file/folder not backed up the issue is with the file or folder permission. The directory does not have the appropriate permissions to access. If the backup encounters a "550 Access is denied" for any file or directory it will skip over and continue the backup.
You will need to set the appropriate permissions for that directory and test with any FTP client such as FileZilla.
Once the appropriate permissions are set the next backup should include the contents of the directory.
To see a complete list of all help articles for Dropmysite, refer to the Table of Contents (TOC) in the Dropmysite – Starter Guide.