This article explains why your iPhone isn't receiving text notifications and how to get it working again.
Restore iMessage Notifications! (Text Notifications Not Showing)
Text notifications are typically handled within the Messages app, which comes pre-installed on all iPhones. When text notifications stop working on an iPhone, it can manifest itself in a few ways:
You might not be receiving text notifications on your iPhone for a number of reasons. If you’re not receiving text messages and you know people have been messaging you, it’s likely a connectivity issue. In that case, make sure your phone is connected to Wi-Fi and mobile data, and that MMS and SMS are set up correctly. If you’re receiving text messages but not notifications, here are the most common causes:
We'll go into more detail about this in the paragraphs below, but we won't discuss notifications from other apps, such as Facebook Messenger and other messaging apps.