Polyline Points are used for Culling in Flat2D mode

When a Polyline is in Flat 2D mode, it renders at zero depth to the local space of the object its attached to; however the points used to render and cull the lines are still at their original world positions (transformed to local space). This means if you're not careful for where your Polyline exists in world space when you add your local points, they may get culled based on their position to the camera.