The first place to look is for duplicates in the input layer, another is bad geometry and a third is a cranky project necessitating moving everything into a new one before running any tool. Assuming they are not a problem, then are the points within the tool's, snapping or the layer's tolerance to the polygon edges/vertices? Of course, there's always just the innate cussedness of ArcMap, and there's no good explanation, just a workaround. I had that with one layer recently which duplicated one point every time, for no good reason.