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Are you playing something on the phone and displaying it on the TV?
Is the Apple TV near the router? If so I suggest you connect it directly using an Ethernet cable and then also restart both the phone and the Apple TV. Other options if your WiFi router supports it is to make a separate SSID for your 5 GHz band and connect both the phone and the Apple TV to use that SSID it is less crowded usually and can be faster
Did you restart both devices?
Are they both updated to the latest software>
Do you have the option of a separate SSID for the 5GHz network on your router?
Also on Apple TV Settings / General / Sleep After: change that to Never
I think the iOS 9.3.1 just came out today
Turn of WiFi on the Apple TV if it is connected by Ethernet which will always be faster and more stable, on the phone go to Settings / General / software Update
I actually have an older Apple TV and a new iPhone 6S I am testing it now to see if it cuts out. The Apple TV is connected by Ethernet and I have my IPhone connected to my 5 GHz network from Apple Airport Extreme
No disconnect until the phone went to sleep for a while