Using external power supply

Is there a way when using external power to watch live video continuously without have to keep pressing continue?

No. Blink does not allow continuous live view. A wired power source other than battery makes no difference to the hardware and app. Some other brands have continuous live view. Don’t hold your breath hoping Blink will do major updates to their system. They are meant to be less expensive entry level cameras with limited basic features.

You just eliminated the #1 function of a Blink camera…totally wireless installation. If you wanted to power a camera via external source, Blink would NOT be the choice to buy. Way too many other choices out there. The Blink mini indoor is powered and needs no batteries. But alas, it still has the limited no capability of continuous live view. operation.