As these things tend to go, it's only a matter of time. HBO is killing off its HBO Go and HBO Now apps on second- and third-generation Apple TV set-top boxes at the end of the month. Respectively, they have A4 and A5 processors, 256MB and 512MB of RAM, and so on. They were released in 2010 and 2012, so the hardware is old.
HBO outlined a few different ways that you can still watch its content. The first and most obvious is to use a different streaming box, such as a newer Apple TV, a Roku, and so on. You can also still use AirPlay from your iPhone, or you can use an adapter and an HDMI cable to connect your iPhone directly to your TV.
One solution that HBO doesn't mention in its support documents is to subscribe to its content through another provider. Amazon and Hulu both offer HBO as a channel, and you can even get it directly through Apple. And if you go the Apple route, you have the added benefit of being able to download content for offline viewing, something that's not even available via HBO's first-party apps and services.
That doesn't help for HBO Go though, which is a streaming service exclusively for people that subscribe to the channel through a cable provider. HBO Now is the standalone service, and despite being named differently, it offers the same content.