Not able use cellular data without on off flight mode

Restart your iPhone or iPad

Restart your device. If you're not sure how to do this, follow these steps.

Check for a Carrier Settings update

To manually check for and install a carrier settings update:

1. Make sure that your device is connected to a Wi-Fi or cellular network.
2. Tap Settings > General > About. If an update is available, you'll see an option to update your carrier settings.
3. To see the version of carrier settings on your device, tap Settings > General > About and look next to Carrier.

If you insert a new SIM card into your iPhone or iPad, you need to download the carrier settings for your new carrier.

Take out the SIM card

After removing the SIM card, put it back in. You might need to contact your carrier:

• If the SIM card is damaged, or doesn't fit in the SIM tray, ask your carrier for a new SIM card.
• If you transferred your SIM card from another device, ask your carrier if your SIM card works with your iPhone or iPad.

Learn more about removing your SIM card.

Reset your Network Settings

Go to Settings > General > Reset > Reset Network Settings. This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before.

Update your iPhone or iPad

Update your iPhone or iPad to the latest version of iOS.

I would bring it to Apple for a hardware diagnostic at this point. Their might be something wrong with the antenna / modem.

Genius Bar Reservation and Apple Support Options - Apple

Also: do your relatives experience the same issue on the same carrier?

There is no reason to switch off Wi-Fi, ever, and several good reasons to leave it on all the time.

But to get to your cellular data question, do you have cellular voice, or does the phone display “no connection” or Searching? And do you have cellular network access at home?

Here’s how cellular connectivity works: When the phone loses its cellular network connection it tries to reconnect immediately. If it fails it waits a few seconds, then tries again. It keeps trying, but the interval between tries gets longer and longer, eventually reaching 5 minutes between tries or longer. It does this because searching when there is no connection uses a huge amount of energy, and if it kept trying and failing it would shorten battery life considerably.

When you put the phone in Airplane mode, then turn off Airplane mode it starts the search process over again, without having to wait 5 minutes. Leaving Wi-Fi on can sometimes shorten the time to reconnect, because it can find its location using nearby Wi-Fi networks (just listening, not connecting to them) and thus know what cell towers to check with. So see if not turning off Wi-Fi speeds up the process.