I've had the same problem for more than a year. Here's what finally fixed it for me:
Use Google’s Public DNS Server To Fix Apple TV Streaming Problems
1. Navigate to Settings >> General >> Network and select Configure TCP/IP.
2. Select “Manually” next to Configure IP.
3. Dont change the IP address or the Subnet Mask and Router Address. Just click "Done".
4. Set the DNS Address screen with the following: 008.008.008.008 and click “Done.”
You should now be able to stream more smoothly on your Apple TV.
If this works for you, please buy a cup of coffee for a complete stranger or some other selfless random act of kindness.