If you open PermitMonitor immediately after lodging your OneCallAccess job, it may take a couple of minutes for the permit request to appear in PermitMonitor.
If it still does not appear, check on your confirmation sheet that the road authority is listed, and has a Status of Permit Request Sent. If it does not, it is possible they are either not registered for the service, or the job does not match the criteria for generating a permit.
In New Zealand:
Some councils have not yet moved over to PermitMonitor and are still using the CAR History system - in this circumstance they will have a Status of CAR Sent on your confirmation sheet. You should contact them with the contact details from your confirmation sheet for further instructions.