Hello, BeeChristine.
Welcome to Apple Support Communities.
From what I've read is that you're unable to keep cellular data turned on for the YouTube app. I'd like to help. Be sure that you're using the latest iOS version and that you've done a restart of your iPhone.
Update your iPhone, iPad, or iPod touch
Restart your iPhone
Then check for any carrier updates: Update your carrier settings on your iPhone or iPad
Also, be sure your apps are up to date.
Check Settings > Cellular > Cellular Data Options and make sure Low Data Mode is not enabled.
If so far nothing works, try to Reset your Network Settings. Tap 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: If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network This article isn't related to your issue but has the steps that I mentioned.
You can also try removing the app and installing it again:
How to delete apps on your iPhone, iPad, and iPod touch
Download apps and games from the App Store
Keep me updated.
Cheers!