IOS Full Device Remote Control
RemoteControl is only possible during MobiControl-App is open.
I think Apple don't release a feature like this.
But it isn't a problem that the status is always disconnected. You can configure how often the devices should be check in and this works fine. In addition to that: If you push a package or configuration all devices check in automatically and receive the new informations.
It sounds like you're having some issues using the Remote Screen Sharing feature. Please contact Technical Support so that they can create a ticket for you.
Remote Control is not possible on iOS. However, with MobiControl v14.2.0 and the latest MobiControl agent, it is now possible to do Remote Screen Sharing without having the MobiControl agent open.