Apps only connect to network when opening

Have you enabled Scheduled Summary?

Settings > Notifications > [Select the App that you are having trouble receiving immediate notifications]

See the pic below for a few examples. Please select immediate delivery.

Go to Settings and tap Notifications. Select an app under Notification Style. Under Alerts, choose the alert style that you want. If you turn on Allow Notifications, choose when you want the notifications delivered — immediately or in the scheduled notification summary.

Use notifications on your iPhone, iPad, and iPod touch

Change notification settings on iPhone

1. Go to Settings > Notifications.
2. To schedule a notifications summary, tap Scheduled Summary, then turn on Scheduled Summary. ... 
3. To choose when you want most notification previews to appear, tap Show Previews, select an option—Always, When Unlocked, or Never—then tap.

More items...

Change notification settings on iPhone - Apple Support (IN)

You can allow access to Notification Center on the Lock Screen. Go to Settings > Face ID & Passcode (on an iPhone with Face ID) or Touch ID & Passcode (on other iPhone models). Enter your passcode. Scroll down and turn on Notification Center (below Allow Access When Locked).

View and respond to notifications on iPhone - Apple Support (IN)

I have some good news, I actually did! So I tried all the suggestions above and none of them worked even restarting the phone.

And I accidentally figured out that deleting and installing the apps again worked. Might sound crazy but i found it out accidentally while I was fixing a glitch on Whatsapp. After re-installing, i got my notifications back and I did that with all the apps that require internet to get notifications and sync; emails, messenger, instagram, etc. And they all worked!

So tried it out maybe and let someone send u a message to test it out. Hope it helps!

Hi, did you perhaps manage to sort this issue? Because I started experiencing the exact same problem on my iPhone a few days ago and I just cannot figure out how to solve it.

Hi Noelleen have you figured it out because my Iphone is doing the same thing.