Text messages

It cannot be the way you have described. Try to find out when it does not give notifications? Under which circumstances for e.g.

• When Locked or Unlocked
• When on DND or Bed Time
• When your Text app is open or closed
• When your ringer is silent or enabled
• For a particular Contact or for all
• For VIPs or for all

If you are never getting a Notification then you need to set up one. --> Use notifications on your iPhone, iPad, and iPod touch - Apple ...

Please check if you have enabled Hide Alerts for a specific message thread / Contact.

Hide Alerts watch the GIF below