Fall detection on Apple Watch 10 to connect to iPhone 17 air

I have an Apple Watch 10 and I have been falling but my watch does not detect my falls. In the past, it would detect it but it wouldn’t let me know till three weeks later. So I’m wanting to know how to fix this situation. My Apple Watch 10 does not have cellular connection. It only has Wi-Fi and Bluetooth connection to my Apple iPhone 17 air. I guess my question is do I have to have Internet on my Apple Watch for my fall detection to work I get supposed to. Thank you.