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.

By being proactive and trying to minimize any of the above factors will lead to a long lifespan. I have many mining GPUs that have 4+ years on them and are still hashing away, and I have several non-mining GPUs that are 6+ years old that still work but are otherwise obsolete.

I think the majority of my GPUs will be replaced not because of failure, but because newer models are always becoming more efficient and a point in time arrives where the mining efficiency is no longer worth the operating costs. This is probably somewhere around the 4 to 5 year mark as some of my oldest cards while still viable for algorithms such as Equihash are really starting to fall behind newer cards, especially those such as the Nvidia 10xx series