To enable background download of emails you need to enable Background App Refresh and Notifications for our app within the app and iOS Settings. Please note that if you force-quit our app, background download of emails will stop working.
Enable/disable Background App Refresh in the iOS settings: Settings > Scroll down to our app > toggle on/off Background App Refresh.
Enable/disable Notifications in the iOS settings, and via our app: Settings > Scroll down to our app > tap Notifications > toggle on/off Allow Notifications.
Edit notifications via our app: Settings > under Mail, tap Notifications > Edit notification preferences per account.
To enable the app badge to update in the background, Background App Refresh and Notifications must be enabled via our app and iOS settings.