No, usually video cards last way longer, defects are usually rare, but it mostly depends on who manufactures it. Like if you had an ECS ATI Radeon HD 5770 it's more likely to be defective (because most ECS products are cheap and usually not reliable) than an XFX ATI Radeon HD 5770.
I have an XFX Radeon HD 4770, I've overclocked it, I spend, to the least, 8 hours a day on my gaming computer (well did, where I'm at I don't have my gaming computer), play mostly every game at high settings, it's hooked up to my TV, a lot of times I leave it on during the night, I've had it for almost a year, and I have yet to have any problems with it. But like Bekkler said, it's best to check reviews and stay away from specific brands, the card I got had some pretty good ratings and reviews, and was it cheap (even cheaper now than when I got it).
A note on ECS, I've had an ECS motherboard for nearly 3 years and maybe it's just luck but it has also been holding up, even though I've been a bit rough with it. Though I think it's time for an upgrade, whenever I can afford it, because my motherboard is bottle-necking my video card, since the PCI-E slot is only 1.0, and my video card is a 2.0 PCI-E card (might as well get a motherboard with PCI-E 3.0 just in case I ever want to upgrade my video card again), I'd also like to at least have a quad core