Define what you mean by "last". If you mean until it breaks, that can never be determined, some cards last 1 year, some will last 10. How cool the GPU stays as well as owning a quality power supply (and quality GPU) can all affect the longevity of the actual, physical hardware.
If you mean how long it'll be able to play games, I'd say you'll be fine for a good some years. You can always turn down settings, and companies don't want to release games that won't run on mainstream hardware.