Are there any natural preservatives that can be used in Soups or Stews?
If cooled and stored properly (minimize air space in the container), most soups will should last in the refrigerator up to 5 days.  Do you really want to be eating the same soup that long?  I would suggest dividing your soups into smaller sized containers and freezing it so you have a wide selection available at any given time.

Depending on the ingredients most soups can be succesfully frozen for long term storage.

Dairy based items are more likely to curdle/separate after thawing so you'd be better to add the cream/milk when you're reheating it.

Chunks of potato or pasta are likely to break up a bit and have a more mealy consistency so it would also be better to leave the potato out and add to it and cook when reheating.