I'm having the same issue. My AppleTV (2) keeps insisting I turn on Home Sharing although it is already on. Everything is up to date and I'm using the same Apple ID on both sides. In fact none of my settings have changed for the three plus years I've had the Apple TV. The problem only came up after updating to Yosemite 10.10 and iTunes 12. It has persisted through:
- Turning off and on Home Sharing on both my iMac and the Apple TV
- Turning off firewall software (Little Snitch and the ports weren't blocked regardless)
- Rebooting the iMac
- Rebooting the AppleTV
- Rebooting the Airport Extreme that connects them (They are connected via ethernet)
Half the time I get the Cannot Connect message and the other half I get the spinning loading animation and then get kicked back to the main screen.
edit:
Solution found: Re: ATV 3 Version 7.0 Home Sharing not woking with Yosemite and iTunes 12
Basically, go into Sharing in your System Preferences and rename your computer.