Reading through the posts in your link, what I find funny is that I would have diagnosed 90% of those problems (initially anyway) as monitor problems, not video card related. After reading through them, the most common thread I can find is power. Either fluctuating power supplies or AGP slots with improper voltages, or both. But then there are the ones who had cards that ATI actually found errors on. As far as I can see THEY did not have bad power supplies or AGP slots.
I think the one poster probably nailed the cause of it, from whichever source. Voltage drop not allowing the card to properly initialise. Whether this came from overheating and damaging part of the card, a bad power supply, faulty AGP slot (which could have been caused by a bad power supply if the power spiked), or just a plain faulty card.
There's more than one way to catch a cold, but once you have it it's the same as anyone else's cold. There's more than one way to fry a video card too it seems.
There are programs you can use to monitor voltages. I use Motherboard Monitor
http://www.pcworld.com/downloads/file_description/0,fid,7309,00.aspIt monitors AGP voltage, CPU voltage, temps inside the case and at the CPU, and fan RPMs. You can also try SiSandra Lite, I think it shows AGP slot voltages. Both are free programs.