Apple TV says internet connection lost, but all other internet devices are fine

This is likely due to a poor network connection where the Apple TV is located. Please do the following:

1. Unplug your modem from its power source and Restart Modem.
2. Unplug your router from its power source and Restart router.
3. Unplug Apple TV from Power for 2-3 minutes – re-plug in and retest. 

Next step is to check the basics in the Apple TV:

• Setting - Network ensure the Apple TV is setup to be on the correct network. If it is then
• Get yourself a tool like iStumbler to measure the network strength where the Apple TV is physically located. If you find the signal strength is low then you may be a candidate for a Mesh network.

I am glad you have a Mesh network. By chance are you using any third party VPN apps on the Apple TV?