I have one of those mini-rice cookers, as well as normal size ones.
The way it should work is, as long as water is in the cooking chamber, heater is ON an temperature rises. As long as there are some water, the temp will never exceed 100 degrees C and keeps cooking. If you look into the cooking chamber, there is a plunger looking thing in the middle. That's a magnetic device. I don't remember the details but it uses the fact that when temp rises beyond certain point, magnetic material loses it's "magnet" and it uses that effect to cut the heat off. Thus, when water is all gone, temperature rises and goes little beyond 100C and power is cut before it reaches temp fuse spec.
My guess is there is something going on with this plunger. Semi-stuck? Battery weakening?
Did you know there's even a ONE CUP version of these cookers? I'm used to large ones. 6 to 10 cups. Those are TINY!