I am having a similar issue. At home on my WiFi network I can see the live feed perfectly. However, at work, on celular data only, I cannot. If I connect to our corporate WiFi it works perfectly but I prefer to keep my device off of the corporate WiFi. Regardless of how I am connected, it always records the events and I can rewatch them, I just cant go live on cellular data.
I also have this same exact issue with Amazon Cam for our interior security. On WiFi it always works and on cellular it never works.
I am using an iPhone X running IOS 13.3 on Cricket wireless (AT&T towers)