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.
If you have had this bug pop up, the best thing to do is to use the Send Feedback feature in the app. This is found on the overflow menu (3 vertical dots) and Help & Feedback. Doing this gets feedback directly to the team responsible for Android Messages within Google and is a more effective way to get issues to them (this applies to any Google app frankly).
While leaving a 1-star review will get your point across public and Google will see it, it has to go through several teams to get to the team in question to fix it.
The bad news is that once you are impacted by this bug, there is no real work around. Rebooting, clearing the apps cache and other common tricks to fix apps in Android are not working. Making it more interesting, other users are not impacted. I, for example, have no problem with notifications working in the app right now (Google Pixel XL on Android Oreo).
Hopefully the Google team responsible for Messages will get a hot fix out soon.