Hi Nariman, it sounds like a bug. If you can please post the .3dm file that contains this object it would help to track down what is happening. (in general posting a model file is a big help, it makes it easier to examine the situation).

The bug is probably triggered because by moving the point probably a sharp crease is forming inside the object. When this happens MoI will cause a surface to be split into 2 surfaces at the crease (which are joined together at the crease line). There is a restriction in MoI where you can only turn on points for objects with more than one surface in them if the surfaces have the same point structure along their shared edges. This should be the case here, but it seems that this part is where there is a bug that you're running into.

As a quick work-around for the bug, select your object that won't have points turn on, and use Edit/Separate on it. This will break apart the object into individual separate surfaces, and you should always be able to turn on points for a single individual surface.

- Michael