Notification backup?
If you do not want to use any third party app, that can read every Notification on your phone then there is a built-in Notification log in Android.
How to enable:
You can see your Notification log under Settings shortcut widget.
Long press on home screen.
Select Add widgets" and select Settings.


Click on Notification log and a shortcut will appear on your home screen to launch Notification log.
That's it. Check details of every notification you missed.
You can't send them back into Notification tray.