The radar works very well when I build it; but after a while I notice the animation stopping, so I go check what's going on and there is a message saying "Radar stopped by a script (or "the script", can't remember exactly).
I delete it, rebuild it somewhere else and It works, then after a while it will stop again with the same message.
Am I doing something wrong? I can't understand, what I do is just plop it and power it.

This is the intended way of working. The radar has a limited range per research level. The radar will re-enable after new range research has finished, until the maximum range has been revealed again.

Unfortunately it is not possible to display a custom message to clarify this and I still have to figure out a way to implement this.

Thank you very much for explaining this. I was about to start research on new levels then I thought "well, but if it doesn't work, what's the sense in doing it". Now I see that there is a lot of sense :D.
I really like the idea of this spiral ribbon going on forever.

I am probably more dense than most people, but adding those few lines you wrote here on the description will save grief to us densies.

In v2.2.0 the radar now shows an icon when the maximum range has been reached. Next to that, when hovering said radar a floating text is generated informing the player to continue research.