Hey BlueSkyBerry,
Welcome to the Apple Support Communities! Thanks for posting about notifications not coming in quite as expected on your iPhone. I'd be glad to see how I can help. Does this happen with all apps or only some? If the issue is specific to a single or a group of apps, make a note of what they are and let me know.
Let's get started by making sure that your iPhone is fully updated-to-date to iOS 13.5.1. Prior to updating, backing your device up is recommended. Learn more about both in Update your iPhone, iPad, or iPod touch. If you're either already updated, or if you have now updated and the issue remains, let's next make sure that all of your installed apps are also fully updated. To look for updates, go to the App Store app, tap on your profile picture in the upper right, swipe down on the middle of the screen for a second or two, and then tap on Update All. once that's done, test again.
Next, let's check you notification settings to ensure that they're all set up as expected and haven't changed. Use notifications on your iPhone, iPad, and iPod touch will walk you through that process. If that's all good, make sure that there are no settings, such as Do Not Disturb turned on that could limit notification alerts. Review Use Do Not Disturb on your iPhone, iPad, and iPod touch for a deeper look into that process. A few other items to check while we're in the Settings app are the date and time and specialty network settings. For the date and time, go to Settings > General > Date & Time and change it to Set Automatically if it isn't already. For specialty network settings, review Use VPN on iPhone to ensure that if there is one set up or installed, that it is turned off during testing.
Hope this helps!
Have a great day.