When accessing imagery via the free Esri ArcGIS Online mapping web application, the maximum zoom level is limited to that of the basemap. This is an Esri ArcGIS Online feature, which is explained here: Choose Basemap.
Since Nearmap imagery is very high-resolution compared to most imagery sources, unless your basemap is Nearmap imagery, you may not be able to see our highest-resolution zoom levels.
To see all available Nearmap zoom levels, you will need to set our imagery as your basemap.
Follow these steps to make Nearmap imagery the basemap:
Sign in to Esri ArcGIS Online at: http://www.arcgis.com/home/webmap/viewer.html.
Open your map in the map viewer and click Add.
From the Add dropdown, click Search for layers.
Select ArcGIS Online from the In drop-down menu.
Enter nearmap in the Find text box.
Click Nearmap US PhotoMaps for US customers, Nearmap AU PhotoMaps for AU customers, or Nearmap NZ PhotoMaps for NZ customers.
Click Use as basemap.
Save your map.
Close and re-open the map viewer page.
The additional Nearmap zoom levels will now be available for viewing.