the cliche, I have tried everything comes to mind. It will snap to the first couple points of like a star per sey. As long as the object is selected.
But the it will stop snapping to any other points. It should snap to any point. Any setting that are specific for this.
I'm make 3d shapes from two stars one in front of another and offset.
In the image I have the pen tool right in the corner where the arrow is, but the pen tools says it would rather me put a node where the yellow box is instead.
I have already made the two dark blue edges but not the long one. As you can see the line I made at the bottom then it stops snapping after this normally I just put up with it.