Apple does not guarantee every notification will be sent immediately. Sometimes they do come a little bit later than the msg arrived in the app. Sometimes it could take up to 10 mins.
Steps to ensure iOS Push Notifications are enabled for the device:
1. Navigate to iPhone's settings
2. Find "Notifications"
3. Scroll until you see "Clientbook"
4. At the top, the "Allow Notifications" toggle should be on (Filled in green)
5. Under "Notification Delivery" set it to "Immediate Delivery"
6. Under "Alerts" ensure that "Lock Screen" "Notification Center" and "Banners" are all selected
If all these steps are completed, and you still aren't receiving notifications, you can uninstall and reinstall the app. Upon opening and logging in you will get the notification, "Would you like to be notified of incoming messages, upcoming client dates and important clienteling reminders?", select "Yes" then "Allow"