The system does not automatically update a property's sale status.
You must update the status manually by clicking the Update Status button on the property overview or the sale pipeline view.
However, you will find that some actions will prompt you if you wish to update the property status in a particular manner which would be typically expected at that point.
For example, when accepting an offer the system will ask you if you wish to update the property status to Sale Agreed.
You can accept the suggested status change, or you can simply ignore this and update it when you are ready.