There are many factors that control the zoom level that a POI first appears at and the interaction of these factors is complex. The following things affect the zoom-level behaviour of Garmin POIs:
The mkgmap style file rules (e.g. resolution 23)
The detail level setting on your GPS or in MapSource
The internal (firmware) based rules which are unknown, but appear to follow a certain logic based on “visibility”. For instance, Garmin hex codes that refer to landmarks typically appear when more zoomed out, when compared to Garmin hex codes for shops etc that you wouldn’t use for navigation.
The order in which these rules apply to a POI appears to be:
Is it in a landmark hex code category? If so, use internal rules to control when it should become visible. If not, use the mkgmap style file resolution and then modify by the detail level setting of the GPS or Mapsource.