According to "Hints From Heloise," as posted in the Washington Post, one should store opened olives or olives from an olive bar in the refrigerator. This keeps the olives fresh for at least two weeks.
It is safe to store unopened jars or cans of olives outside the refrigerator in any area not exposed to temperature extremes. After opening, placing olives in a glass storage container, covering them in their own brine and storing them in the refrigerator keeps them moist and fresh and prevents discoloration. When selecting bulk olives from a bar, one should pour a little extra brine into the container to cover the olives. The storage recommendations are the same for both green and black olive varieties.