Hi
Apple Watch Series 3 (GPS + Cellular) will only attempt to connect to the cellular network if it cannot connect either to the paired iPhone via Bluetooth or, as a first fallback, to a compatible Wi-FI network:
- About Bluetooth, Wi-Fi, and cellular on your Apple Watch - Apple Support
- Use Apple Watch with a cellular network—Apple Watch Series 3 (GPS + Cellular) only
- How to use your Apple Watch without your iPhone nearby - Apple Support
It may help to follow the steps here, including under the heading "Get help if you can't send or receive messages":
Read and reply to messages with your Apple Watch - Apple Support
If you have not yet done so and if the feature is supported on your carrier plan, you may also wish to enable Wi-Fi Calling on your devices:
- On your iPhone, go to: Settings > Phone > Wi-Fi Calling.
- On your iPhone, in the Watch app, go to: My Watch > Phone.
- Make a call with Wi-Fi Calling - Apple Support
Otherwise, if your Apple Watch is not connecting or remaining connected to cellular as expected, then in the first instance I suggest that you contact your carrier for assistance.
If the issue persists and depending on your carrier's advice, I suggest that you next contact Apple Support (remote diagnostics and/or mail-in service may be available, if required), make a Genius Bar reservation or visit an Apple Authorised Service Provider for assistance: