So you are editing the record and saving it when it should be triggering the Past Due rule right? If the record is not being edited and saved again during the time it is past due then nothing will change when doing this with form rules.
If you want your dropdown to be dynamic and change as data changes and time passes then it will need to be a formula field and take into account all the possible changes you want to see. Then people cannot explicitly change the Status on their own though, only through data changes.
