Disappearing AirPlay icon on iPad 2, iOS 7.0.4

I'm hoping someone can help me with an issue we are having when trying to use AirPlay Mirroring on an iPad 2, running the latest version of iOS (7.0.4).

When I swipe up to reveal the "Control Centre" (also available in "Settings", I believe), most of the time, the AirPlay icon is not there. Twice (once last night while running iOS 7.0.3 and once this morning running iOS 7.0.4) I was able to see the AirPlay icon, so I clicked on it, told it to mirror the iPad screen to my Apple TV (connected to the same WiFi network through the same router) and, because there was no "done" button like some tutorials suggested, just clicked elsewhere on the iPad "whitespace" to activate the settings. Last night, nothing happened - no mirroring on the Apple TV. This morning, I was able to see the iPad home screen on the Apple TV and bring up Safari but as soon as I tried to bring up a "Nature of Things" documentary and stream it (which is available for free to me in my geographic location as I am a Canadian resident/Internet user), the Apple TV lost the iPad mirror and reverted to the Apple TV home screen.

I tried rebooting the router, have updated the iPad 2 to run iOS 7.0.4 (we'd been delaying the update as we were not impressed with the updated look & feel and overall user experience of iOS 7 compared to what we felt was superior, its iOS 6 predecessor). I have also tried to use mirroring both with Bluetooth enabled and also with Bluetooth disabled, after reading some online discussions on this very message board. One thing to note, though, after disabling Bluetooth both on the Apple TV settings and in the "Settings" menu of the iPad, when I swipe upwards to active the "Control Centre", the Bluetooth icon keeps lighting up so I have to keep disabling it. Any idea why? At any rate, the AirPlay icon still does not appear when activating "Control Centre" most of the time. Why did Apple make the AirPlay icon only appear some of the time? That is NOT very user-friendly - a better implementation would be to (a) make it available in the "Settings" menu, in "Control Centre" all the time and (b) when AirPlay cannot be used (i.e., no WiFi connection), have a prompt/dialog box explain why.

I don't think it's a networking issue because Internet access is fine on other computers or when surfing the Internet via the iPad only (no AirPlay mirroring) or watching a movie using the Netflix "app" on Apple TV.

My questions are: (a) why does the AirPlay icon only come up very occasionally (twice)? (b) when it does come up, why so short-lived? and (c) is there supposed to be a "done" button once the AirPlay icon is visible and you've selected which device to mirror to?

Your answers are much appreciated! 🙂

Thanks,

Doug M.

P.S. As an aside, why does Apple not allow you to add other "apps" (i.e., icons) to the Apple TV home screen, like you can with an iPad or other iOS-powered device? Any idea if they might add that functionality?