I have a very similar issue since updating to 10.10.5 on a Macbook Pro (13 inch, mid-2012). This was not an issue previously and I haven't changed any settings. I have the latest Apple TV 3, purchased in the last few months.
Our issues manifest slightly differently - I can see Apple TV as an option under displays but I can't manage to connect to it. I get the message: 'Could not connect to 'Apple TV'. This happens whether I try to connect via the display drop down, or the alt sound drop down. Once or twice, I have also been asked for a confirmation passcode that the Apple TV is supposedly outputting - it isn't. My iPhone 6 (since the equally recent 8.4.1 update) doesn't now see Apple TV in the control centre (the menu that slides up from the bottom) either.
What I have noticed is that this inability to connect only seems to happen when the Apple TV is on standby. Tellingly, I can use the Apple TV remote to wake it and THEN connect on either the Macbook or the iPhone, and everything works fine.
Our issues seem to me too much of a coincidence. If I had to take a guess, I'd say that these latest software updates have affected certain devices ability to connect to Apple TV while it is on standby.
Separately, video performance continues to be choppy on VLC (or any video app for that matter) streamed via Apple TV. I've had to purchase Beamer, which demonstrates that perfectly smooth video streaming clearly is possible on my network setup, just not properly implemented in Yosemite. Spotify audio suffers to a much lesser extent but is still not perfect - I'd buy Airfoil but out of principle I don't see why we should have to pay for even more 3rd party software to provide functionality that should be a given with our products and software. I heard this all used to work fine in previous OS X Mavericks - let's hope it gets fixed with El Capitan, but I'm not holding my breath...