I just checked your site and it seems like the ‘admin_body_class’ filter is not called on the Invoice add/edit pages. As a result, Invoicing is unable to hide the default WordPress publish metabox which causes WordPress to mark new items as published.
This is not a bug with Invoicing. It is probably a conflict with another plugin. Try disabling each plugin one-by-one to figure out which one is causing the issue.
To open a new support ticket, first select the relevant forum and then click the "New Post" button. Example: You need support for the core plugin? Click on Core Plugin support and click on the "New Post" Button.