Ensuring iOS user notifications work during the development phase

I am testing an app on my phone that schedules user notifications; when my phone is connected to my computer and the app is running in Xcode, the notifications work every time.

The problem is that when I stop Xcode running, the app icon is left on my phone and everything on the app that I put in it is still there, and the notifications work for maybe a minute before they don't work anymore. What I am worried about is that if I publish the app it will work as the former where it works for a few moments then no longer.

How can I test these notifications so that I know they'll work when I submit to the App Store?