When coating a weapon with poison the on-hit effect only work for the first strike you make. Yet the on-hit effect remains on the weapon for a time, even over rest, during which if you re-coat it with poison, nothing will happen.
I tested this by using poison on several weapons, on each the poison took effect on the first hit landed but I never saw it repeat it self.
Not sure how they are intended to work but probably not like this.