Never had kibble last long enough to find out. (I go through 40 lbs every week)But, if it were me, I wouldnt have it open for more then 2-3 weeks. Buy just enough to last you that long.
We did have kibble go bad on us once- mice chewed a hole in the bottom of the container, and it got wet. It had a rancid smell, like something was rotting. (Which it was). Go by the smell on it. If it smells nasty, or unusual, throw it out.