I'm happy with my GE portable induction cooktop (single burner). I have two 8" pans (one cast iron, one induction-certified Oxo) and one induction-certified 12" pan (Nuwave) that work great. I've tried three induction-certified 10" pans and none work! Oxo, Sensarte, and Green Pan brands. Is it possible that my induction cooktop is incompatible with 10" pans???
Induction cookers are tricky. They heat with a donut-shaped antenna under the glass top. You have likely noticed a circular "hot spot" in your pans. This is the size and shape of the underlying antenna. Consumer induction cooktops all have single-donut antennae. Commercial units, which can cost more than 10X as much, usually have two concentric "donuts" for better coverage.
The circular graphic on the stovetop is not necessarily centered over the donut antenna. My Frigidaire induction has one graphic a full inch off-axis. You can tell by putting 1/8" of water in a large cast iron frying pan and putting the burner on "hi". The circle of bubbles will identify the center of the antenna. Center your pot there, not over the graphic.
The burners have sensors to determine if a magnetic pot is correctly located above the antenna. That's why they "know" to turn off if you lift the pot. And why burners will sometimes refuse to heat small pans, especially cheapies.
Your misbehaving pans may be "induction compatible", not "induction optimal". Laminated pans which are optimized for induction are more expensive to manufacture.
I suspect it is this "safety" sensor which is causing mischief. If a cheapie pan is off-center from the antenna, the cooktop may interpret that as "no pot present".
The magnet test is helpful, but not foolproof. Trust in cast iron. All other pots must prove themselves.