Hello @Wirehead 

Thank you for your feedback. 

• Please try to leave only one phone to stream Camera and see if the ' Continue live stream' message pops up?
• Turn off VPN on the phone
• Turn off mobile data on the phone 
• When 'Continue' message occurs, try to ping camera's IP address on the phone and see if the ping failed or not, refer to Step2 in guide here to ping camera: 

https://www.tp-link.com/support/faq/3261/

If still the same, may I know the model of router, and network topology: e.g. ISP XX - router model xx <wireless>camera;  router <wireless> mobile device, thank you~