To ensure the prompt delivery of WhatsApp notifications, your phone must be configured properly.
Make sure that WhatsApp notifications are not muted in WhatsApp settings and in each chat:
Open WhatsApp, tap More > settings > notifications and make sure that message and group notifications are set to On.
Open the chat you wish to receive notifications from > More > group info or info and make sure the chat is not muted.
Notifications on Windows Phone require a strong network connection; if your phone has a bad Internet connection or is on the edge/outside of a coverage area, it may take some time before WhatsApp is able to reconnect to your phone and deliver notifications.
If the Battery Saver is enabled, notifications will not be delivered to conserve the battery. Make sure the Battery Saver mode is turned off under Windows Phone Settings > system > battery saver.
Ensure WhatsApp is pinned to Start. That way, if you miss a notification, you can still see an unread message count on the live tile.