Make sure you have push notifications enabled for the teams you would like to receive notifications for. You can do this by selecting "Account" in the bottom right of the nav bar. Select "Notifications" to alter your preferences. Please note that Story push notifications are only sent out when our editors select a Story to push. We are working on a more robust push notification feature set.
If you are not receiving Game Results notifications, it is likely that your device was incorrectly enrolled in our push server. Please uninstall The Athletic app and reinstall it to fix this problem.