After an update rolled out to the app late last week, several users are reporting that notifications in Android Messages is no longer working. The update in question is version 2.5.207 users are reporting that the SMS/MMS app simply stops giving notifications and there is no way to enable them again. Indeed, the app will indicate that notifications are enabled but none are given to users.
The problem appears to be widespread. Multiple reviews within the Google Play Store indicate that notifications have quit working across multiple devices and Android flavors.