You can hide any device that is connected to Reflector. Hiding a device will not disconnect it, but will prevent it from being shown on the screen. As long as the device stays active and doesn't fall asleep, the device will be connected and can be show at any time.
To hide a device, open the Reflector 2 menu. Click the blue eye icon to hide the device. The icon will turn gray to signal the device is hidden.
To begin showing a hidden device again, click the gray icon.