2/5/2013 at 3:19 p.m. (4 months, 2 weeks ago)
Recently the AppleTV 5.2 update was released and I found both of my AppleTV 3 devices failing to apply the update consistently. This is not to be confused with the 5.1.2 update which had a specific issue with updating the device via ethernet connection (fixed in 5.2).
The solution that I identified was to restart my AppleTV (under settings->general->restart), and after restart apply the update immediately. I guess using the device as intended must use memory or other resources in a way that cause the update to fail.