You can keep live, refrigerated oysters for one to two days. They can be eaten as long as they are still alive. Always check the shellfish for signs of life before eating. How you store live oysters is by covering them with a damp cloth to keep them from drying out. Shelled, or shucked, oysters can be kept at 35 degrees Fahrenheit or less for up to 7 days, or by the 'use by' date.