Retrieve missed push notifications

On iPhone if I accidentally open an app before I've gone through the app's push notifications, the notifications disappear. However, I'm not sure if they're gone forever as I've noticed a bug with one app in which old push notifications sometimes reappeared. Although the apps in question that I would like to be able to retrieve recently missed push notifications for are different than the one with the bug, it still makes me wonder whether push notifications in general are stored somewhere on the phone even after an app is opened. If so, I would like to retrieve these as the information provided by these notifications cannot always be found in the app. I've tried disabling then reenabling push notifications but that didn't work. Thanks for any help.