New to Apple TV - struggling with AirPlay and Home Sharing
The design of iOS isn't helping you troubleshoot this issue since it suppresses the AirPlay icon until a device detects a receiver on the local subnet.

Just being on the same network isn't enough, the devices need to see broadcast traffic that works best with IPv6 support and can also work when you only are routing IPv4 traffic.

The simplest thing to do is power off the extender and see if you can confirm that the two devices see each other.

Sadly, I don't see this documented well by Apple, but here is one article that explains you might not see the AirPlay icon due to network issues:


http://support.apple.com/kb/TS4215