The Help link is using a function called window.showHelp to open the link to the Help page. Internet Explorer has a check on the security zone of the URL when you call window.showHelp. If the security zone is not in the Trusted Sites zone, then Internet Explorer will handle opening the resource itself.
But when the website is added to Trusted Sites, then Internet Explorer will hand the URL to the HTML Help ActiveX control to perform the navigation. The HTML Help ActiveX control has a check to see whether the URL is an http URL. It only lets an http URL to make the navigation, and it will block an https URL. This behavior is by design.