Have you disabled MAC address randomization for you home Wi-Fi network in iOS? (it's called "Private Wi-Fi address" or something like that in specific Wi-Fi network properties)
If not, SHIELD probably recognizes your phone as different device each time you connect, since each time new MAC address is generated, so it requires new authorization.
Uninstall that app (it's dead) and use the remote in the Google TV app (formally known as Google Play Movies & TV)