It's the solder - when the chip gets too hot it melts the solder, and if you are dead careful, it is possible to reflow the solder and fix it. It's basically the same problem that cause Xbox360's RROD.
Cheap cooling is often the cause, cheaper cards with nasty little fans on them will never last - go for the card with the most cooling hardware hanging off it. If the chip was held in place it would probably just burn out - it's when people quickly switch their PC off that saves it from the serious damage.
Really they need to find a viable alternativ to solder, if solder can't cope with working temperatures, then they need to use more sockets, like with processors - it's rare for a processor to have issues like this.
Too much cost cutting, not enough burn-in testing, and designing for speed rather than reliability are to blame. Personally, if I had a guarantee that a graphics card would still work in 3 years time, then I'd be prepared to spend more.