3 years?
As has been said many times already, a properly cared for GPU can have a indefinite life-span with usually the part becoming obsolete before failing. This can easily mean 5+ years of operation.
Most GPUs that have some defect from manufacturing or installation damage will usually fail within the first month or so of continuous operation, which since is within the warranty period usually pose no problem other than the inconvenience of doing the RMA.
Other factors that can lead to failure have been mentioned already in the thread, but normally boils down to the care one takes to maximizing their longevity. Electrical problems (surges, brownouts, static discharge, loose connections, bad or unstable PSU) are probably near the top of the lists, along with excessive heat (higher than 80° C operating temperature), dust, dirt, humidity, and of course physical damage.
Long term, FAN DEATH is the leading cause of card failure for cards that make it out of infant mortality.
I've got several HD 7750 and a 7870 that date back to LITECOIN GPU mining days - they've been in pretty close to continuous usage that whole time (4 years now almost), doing mining or Distributed.Net work (which offers a VERY similar load to most cryptocoin mining algos as it IS crypto work as well).
Had to replace the fans on all the HIS 7750 cards (junk sleeve bearing fans) in less than a year, the Sapphire HD7750 JUST had it's (ball bearing) fan die last month, and the HIS blower-type card is still going strong on the original fan (ball bearing LOW loaded big-bloody-blower, it's the IceQ model).
Everything I had before that point was either ancient pre-Stream pre-CUDA, or AMD APUs.