You would need to add an additional field per row. This could be a row number and then you could make a conditional rule that would only allow them to edit the last row or max(row number).
You also could add a username field instead. This would allow them to edit all of their entries rather then just the most recent.
With an Active Directory Web Service you could identify each form user and then match their user name to allow edit. This would also give you an audit track of who updated what.