You need to store boiled eggs in airtight containers to keep the odor of the eggs from lingering in the refrigerator. The boiled eggs will not last as long as raw eggs. You can safely consume properly refrigerated boiled eggs for one week before you need to discard them.lace the container in the refrigerator. If you wish to peel the eggs before you store them, then submerge them in a covered bowl of cool water. Discard the eggs after one week in the refrigerator.