I used to do research in the animal byproduct field specializing in fats and oils. Allen's comments are right on the money. But know that all fat oxidizes over time - that's what causes rancidity. Heat, light, water, food particals and as mentioned - salt all increase the rate of oxidation. However fat (oil) can be stored in the freezer in an opaque container for several years with no noticable deterioration. Used oil should be strained before storing.
One other note. High temperatures causes an increase in transfatty acids. The chemistry is complex, but from a health standpoint, if you are cooking at about 350 degrees, I wouldn't restore that oil more than twice. Oils with a higher titer will do better (peanut oil, coconut, or a blend) will do better. Hope this helps - probably more than you want to know.
I'm just an ornery sinner saved by Grace:o