How to make a plane well defined before, always well defined after ?

I thought at first that offsetting a spline of 10mm would be easy and smart to modify a whole part.

It's awful, with this SW12.

I define a plane with 3 points.

I make after that a surface cut.

So, 2 points out of 3 are eaten with this cutting.

And then, the plane turns out in red : "the point to define the construction plane is no longer in the model !!!!"

What is this kidding ? Of course the point is in the model, since there is a surface cutting of something, the something appearing on my screen.

So how can I keep up this plane, after any cutting ?

SolidworksSketching