UI on WorldToScreenPoint doesn't work on certain camera angles

I have a scene with a plane in Unity. I am using the following code:

     Vector3[] vertices = new Vector3[choices.Count];
     Vector3 center = Camera.main.WorldToScreenPoint(targetPos);
     float angle = Mathf.PI * 2 / vertices.Length;

     for (int i = 0; i < vertices.Length; ++i) {
         float verticeAngle = i * angle;
         vertices[i] = center + 100 * new Vector3(Mathf.Sin(verticeAngle), Mathf.Cos(verticeAngle), center.z);
     }

     for (int i = 0; i < vertices.Length; ++i) {
         var btn = Instantiate(prefabChoiceButton) as GameObject;
         btn.transform.SetParent(canvas.transform, false);
         btn.GetComponent<RectTransform>().position = vertices[i];
     }

where targetPos comes from:

     Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);
     RaycastHit hit;

     if (Physics.Raycast(ray, out hit, 1000, (1 << 8) | (1 << 10))) {
         // here I call targetPos with hit.point
     }

The buttons showed fine so far, but I changed the camera angle and now they don't show up (they show up when I get to the old camera angle). In both angles I can clearly see the plane, they are not far away from each other.

Working camera settings:

 Position (0, 5, -6)
 Rotation (60, 0, 0)
 Field of view 60

Angle not working:

 Position (0, 10, -6)
 Rotation (60, 0, 0)
 Field of view 60

What is even weirder is that sometimes even if I can't see the buttons, clicking randomly sometimes triggers the click event on them.