Why aren't distances updating as I walk down the fairway?

This is likely because you have GPS Mode turned 'Off'.

Please make sure you have Location Services in High Accuracy:

Settings > Location > Enable **Location** > Select **High Accuracy** mode

Hole19 has permissions to use location?

Settings > Apps > Hole19 > Permissions > Enable Location Permission

Note: If you are playing in Advanced Mode, Tap the ‘More’ icon (3 dots), go to settings and turn the 'GPS Mode' toggle 'On'.