You should make sure your device battery has power and your device is connected properly to the app. Your app must be running in the background for notifications to properly work. If the problem persists you may unpair your device from the phone and pair it again. If you are wearing another smartwatch device that is receiving notifications (e.g. Apple Watch, Pebble, etc.), the notification may not always go to both devices, and can in some cases only go to one of the devices, but not the other.
iPhone users: Go to your phone's settings and tap Notifications. Scroll down to Messages, then scroll down to Options. When you tap Show Previews, either choose Always or When Unlocked. If Never is selected, your iPhone won't push the messages to a paired device.