I found the following information for you to try out:
If you are experiencing intermittent playback or significant network lag with AirPlay or AirPlay Mirroring, it could be due to a weak Wi-Fi connection, interference, or the distance between the Wi-Fi router and your iOS device, Apple TV or AirPort Express.
Try the following suggestions:
- Ensure that other devices are not trying to stream to the same Apple TV at the same time.
- Turn off Bluetooth on your iOS device by tapping Settings > Bluetooth.
- Ensure that your Wi-Fi router is set up with the recommended settings for the best performance.
- Certain external devices, such as microwave ovens and baby monitors, may interfere with a Wi-Fi network. Try moving or disabling these devices.
- If possible, try to locate your Wi-Fi router in the same room as your iOS device and Apple TV.
- If your wireless and wired networks are the same, try connecting your Apple TV to the router via Ethernet instead of Wi-Fi.
- If the Wi-Fi router has an external antenna, check to see that is it connected properly and in good condition.
- Use the Wi-Fi network troubleshooting guide to resolve interference and other issues.
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