Both cooked and raw breakfast sausage will last up to 4 days in the refrigerator before it goes bad.
If you have any breakfast sausage that you want to keep longer than 4 days then put it in Ziploc bags or freezer safe containers and freeze it.
When frozen the breakfast sausage or any other sausage will keep fresh for up to 6 months and it will last up to a year before it goes bad.
Freezing the sausage including breakfast sausage helps to keep bacteria from growing on it which makes it last longer.
But if you plan to eat the breakfast sausage or any other sausage within 4 days then keeping it in the fridge is good enough.