I started bringing a travel router (doubles as extender @ home) to connect my Apple TV. Previously, I just needed to complete the WIFI connection on my iPhone. However, in the past year, the captive portal gives me the "server does not respond" message.

In the times when I forget to bring the router, all it took was a call to the hotel's provider to get my ATV whitelisted. They mainly need the IP and MAC address, after which I restart the ATV, and I'm good to go.