[Solved] Two meshes work fine separately but can't be rendered simultaneously

I have a component that generates a mesh representing unit's field of view. Method Generate is called inside the Awake() method of the FieldOfView component. I also have two different prefabs containing this component. Now the strange thing happens:

• If I instantiate only one of these prefabs (no matter which one of two), its field of view is rendered properly.

• If I instantiate both of them, neither one is rendered.

• If I instatiate two copies of a single prefab, neither one is rendered.

• If I instantiate both of them and start the game, then pause and switch FieldOfView component off in the inspector for one of them (again, no matter for which one of two), the mesh of the other game object is rendered.

Please, help me figure out what can be the reason for this awkward behavior. Please, see FieldOfView component code below:

 using UnityEngine;
 
 namespace Assets.Scripts
 {
     [RequireComponent(typeof(MeshFilter), typeof(MeshRenderer))]
     public class FieldOfView : MonoBehaviour
     {
         private const int Steps = 10;
         private const float HeightAboveGround = 0.5f;
 
         [SerializeField] private float _barColorRed;
         [SerializeField] private float _barColorGreen;
         [SerializeField] private float _barColorBlue;
 
         [SerializeField] private int _maxDistance;
         [SerializeField] private float _fieldAngle;
         private Mesh _mesh;
 
         private void Awake()
         {
             Generate();
         }
 
         private void Generate()
         {
             GetComponent<MeshFilter>().mesh = _mesh = new Mesh();            
             Vector3[] vertices = new Vector3[Steps + 2];
             vertices[0] = Vector3.zero;
             int cnt = 1;
             for (float angle = -_fieldAngle / 2; angle <= _fieldAngle / 2 + Mathf.Epsilon; angle += _fieldAngle / Steps)
             {
                 float x = Mathf.Sin(angle * Mathf.Deg2Rad) * _maxDistance;
                 float y = Mathf.Cos(angle * Mathf.Deg2Rad) * _maxDistance;
                 vertices[cnt++] = new Vector3(x, HeightAboveGround, y);
             }
             _mesh.vertices = vertices;
 
             Color barColor = new Color(_barColorRed, _barColorGreen, _barColorBlue);
             Color[] colors = new Color[vertices.Length];
             for (int i = 0; i < vertices.Length; i++)
             {
                 colors[i] = barColor;
             }
             _mesh.colors = colors;
 
             int[] triangles = new int[(Steps + 1) * 3];
             for (int i = 0; i < Steps; i++)
             {
                 triangles[i * 3] = 0;
                 triangles[i * 3 + 1] = i + 2;
                 triangles[i * 3 + 2] = i + 1;
             }
             _mesh.triangles = triangles;
 
             _mesh.RecalculateBounds();
             _mesh.RecalculateNormals();         
         }
 
         public bool IsInField(Vector3 position)
         {
             Vector3 to = position - transform.position;
             float distanceToTarget = to.magnitude;
             float angle = Vector2.Angle(new Vector2(transform.forward.x, transform.forward.z), new Vector2(to.x, to.z));
             return distanceToTarget < _maxDistance && Mathf.Abs(angle) < _fieldAngle / 2;
         }
 
         public void Die()
         {
             if (_mesh)
             {
                 _mesh.Clear();
             }
         }
     }
 }
 

upd. Here is the link to a screencast on which you can see what exactly happens: https://drive.google.com/open?id=1jKpPbFDQXeXBtYPfZ8uNWe2k1OC_D4Fd

upd2. See the solution in the comments to the answer by Buckslice.