Hello hoptod,
Welcome to Apple Support Communities!
We want to make sure your notifications are working as excepted.
Double check that your settings are correct with these steps:
"Manage notifications for messages
- Go to Settings > Notifications > Messages.
- Choose options, including the following:
- Turn Allow Notifications and immediate delivery for Time Sensitive Notifications on or off.
- Set the position, locations, style, and sounds for alerts.
- Choose when message previews should appear on the Lock Screen, and how they should be grouped.
- Set how many times to repeat an alert (from Never to 10 Times) below Customize Notifications.
See Change notification settings on iPhone."
This Apple Support page has the full details: Change message notifications on iPhone - Apple Support
Since it sounds like an issue with SMS only, are you using iOS 16.3 when this happens? If all updates are installed, please reach out to an Apple Support Advisor for further assistance: Get Support
We hope this helps so they can isolate the source of the issue.
Cheers!