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:

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

Hole19 has permissions to use location?

Phone Settings > Apps > Hole19 > Permissions > Enable Location Permission

You can always turn 'On' the GPS during your round. You just need to tap the bottom button, tap 'Settings' and turn on the 'GPS Mode' toggle.