For NZ citizens, the subclass 444 visa is cancelled when they leave Australia and a new one issued when they arrive back in the country. In most situations where this result is returned for a NZ citizen, the person is currently out of Australia which is causing the 'No Valid Visa' VEVO check result.
Check to see if the person is in Australia or not. You can run another VEVO check using CWR when the person has confirmed that they are in Australia which will most likely update this status.
CheckWorkRights automatically recheck any active candidates or employees with no valid visa every 72 to monitor for an update from Department of Home Affairs.
If the candidate or employee is onshore in Australia and their record is still showing as ‘No Valid Visa’ the NZ citizen will need to contact home affairs to ascertain the reason, and to have a new visa granted.