Which circumstance will prevent a system administrator from deleting a custom field?

The dialog box is in the way, or the field is part of a field dependency and if the delete box is unchecked so that users cannot delete something from a folder by accident. Ability to remove something from a folder usually depends upon the permissions assigned by the parent and not the folder itself.

The ability to delete is also dependent upon certain commands. If you try to delete the main folder, you will erase everything inside except the special folder or file. Also, if the key folder is protected, then you cannot delete the custom field.