Assuming you are referring to an ordinary coffee cake made with flour, sugar, butter, eggs, and baking powder, it will keep fresh for 3-4 days. Coffee cake is best stored in an airtight container at room temperature. If you want your coffee cake to last longer than a few days, you can freeze it. Wrapped tightly in plastic wrap or aluminum foil, coffee cake will keep in the freezer for 2-3 months.