Why is my Apple TV not updating?

I have a Revision A 3rd Generation Apple TV.

It’s working fine with my TV: and receiving a signal from both my MacPro and Mac Mini. However, I’ve tried updating it from the current version of the software — 6.2, I believe — to version 7. Each time, I’m told that the update cannot be downloaded. Even after I’ve restarted both it: and my router.

What’s happening?