Hard-cooked eggs in the shell can be refrigerated up to one week. Peeled hard boiled eggs can be stored in the refrigerator in a bowl of cold water to cover for about 1 week (change the water daily) - or in a sealed container without water (cover the eggs with damp paper towels) for the same length of time.n egg that is at room temperature at the start of the cooking process will require about 1 minute less cooking time than eggs taken directly from the refrigerator. 4. Technique for hard-cooking (boiled) eggs: Choose the right size pot to cook your eggs in: The eggs must not be stacked but be in one (1) layer only.