Why would a portable heater set off a carbon monoxide alarm?
If your carbon monoxide alarm is going off, you need to assume that there's actually carbon monoxide in dangerous levels in that area. If the heater is electric it probably shouldn't be emitting CO but maybe there's a manufacturing defect that's causing the heating element or plastic to burn.

CO is lethal and totally undetectable by people, so if the alarm goes off you need to leave the building and open the windows. The absence of smoke does not mean that you are safe.

(CO detectors have a limited lifespan: 2-10 years, depending on the model. There should be a date stamped on it somewhere. If it's at "retirement" age you should probably replace it anyway, and then you can see if the new one still goes off.)

Revision based on question update:

You must not ignore the CO detector. People can and do die in their own homes of CO poisoning, oblivious to the problem. Unlike smoke/fire, there's no way for you to tell the source of the problem or evaluate its severity, and no way to tell if the problem has been resolved. You probably have a sub-standard or defective heater — I would not use it anymore.