Have you checked your Access settings for this form?
Go to Toolset > Access Control > Front-end Forms and check which roles can do what for this form, making sure you have granted the required permissions.
If you already have and it is not working, let me know.
Are you actually deleting posts? The settings for deleting posts apply to all forms, the other settings are specific to individual forms.
I understood that we were talking about the "Visitor cancel" edit form which changes the status of the post to draft, and you have not specified any role other than Creator to be able to use that form.
It's in the screenshot you shared with me. Please read the titles of the columns, you are looking for Edit Own (or Others) Custom Post with the Form "Visitor Cancel".