OnTriggerExit won't detect player?

Hey everyone! I'm having a small problem with my collisions. You see when I enter the collision area it works fine and the collision becomes true but when I leave it it doesn't go back false. Any of you got any ideas why? Here's the code!

 using UnityEngine;
 using System.Collections;
 
 public class RunAfter : MonoBehaviour
 {
     public Transform targ;
     public Transform body;
     public bool player;
 
     void OnTriggerEnter(Collider other)
     {
         if (other.tag == "Player")
         {
             player = true;
         }
     }
 
     void OnTiggerExit(Collider other)
     {
         if (other.tag == "Player")
         {
             player = false;
         }
     }
 
     void Update()
     {
         if (player == true)
         {
             body.transform.Translate(Vector3.right*0.15f);
         }
 
         transform.position = new Vector3(body.position.x, body.position.y, body.position.z);
     }
 }