Airplay works fine, the rest only sometimes

I recently got an apple TV. I've got it hooked up as follows:

+--------------+ +-------------+

| | +----------------+ | |

| Apple TV | | | | TV |

| +----->| +----->| |

+--------------+ | | +-------------+

| AV Receiver |

+--------------+ | | +-------------+

| +----->| +----->| |

| Cable box | | | | Speakers |

| | +----------------+ | |

+--------------+ +-------------+

The receiver has multiple HDMI inputs and switches between them.

I can use the Apple TV as an airplay receiver for audio and video content stored on my Mac, and control it through the iOS "Remote" app (and to be fair, that's mostly how I use it). That part is fine. It also rolls over to the cascading-photos screensaver if I leave it alone.

However, the Apple TV's native interface for picking online services, navigating media that is available via Home Sharing, etc, is erratic. If I disconnect it from power and reconnect it to force a restart, that part works fine, but after one or two sessions, the screen is black when I try to access it. Using the remote, I can hear the Apple TV making its usual feedback sounds, so something is happening, I just can't see it. I would prefer not to need to force a reboot every time I wanted to use it.