In Many case AirPlay icon didn’t works or show/ Enabled on control center when your iPhone locked or unlocked. For batter access Apple gave Airplay icon in control center so you can easily enable and start entertainment without delay in establish connection between your iOS device and AirPlay enabled remote devices. Some of the time you can’t see AirPlay icon in control center or AirPlay icon missing in iPhone 6S / 6S plus due to internal error or connection problem/ AirPlay Settings and Not supporting devices.
In the case for remotely play audio and video file to your other devices at your home or office network without cable, wirelessly through AirPlay.
Best Air Printer for iPhone, iPad & iPod Touch: Remotely print
AirPlay compatible devices: Streaming from iPhone, iPad and iPod touch to Media devices (2nd Generation Apple TV, AirPlay Speaker, AirPlay Receivers)
Fixed: Alternate solution for AirPlay icon missing in iPhone 6S, 6S Plus
Poor connectivity cause one of the main reasons behind AirPlay icon not showing/ Disabled from control center. So keep your both sending and receiving devices near to possible.
AirPlay doesn’t support parallel connection between more than one iOS devices to single AirPlay device. So you can’t connect another device for sharing photos, Videos or audio to AirPlay device.
Update device: Check and Update your iOS device
Keep your Apple Device up to date with new iOS version (Setting > General > Software Update). And from Apple TV (Setting > General > Software Update) and more about update TV OS.
Disable or Enable: AirPlay from Apple TV (Setting > AirPlay), Restart your both device for reconfiguration internet setting or remove data packets from network.
Check router configurations
Remove AlterNet WiFi device
Any other Wi-Fi device running synchronously, that time your device auto detect and connect on poor connection with other network, So you might lose AirPlay connectivity.
Hope this will help, Most of the possible solution are listed above, Best of luck for AirPlay icon missing in iPhone 6S, 6S Plus, 6, 6 Plus, 5S on iOS 9.