jumping from ledge problem

My movement script allows the player to jump 0.1s after going off a ledge so that it seems more realistical. Otherwise he would just slide off the ledge as soon as he reaches it. I have a Capsule with CharacterController.

The problem is that the player wont jump sometimes when on ground. It happens just once in 20 times but it happens and it would be irritating if it'd happen at a crucial moment. I tried the code without the ledge tolerance and it works perfectly fine but does someone have an idea how to solve the problem or does someone have an alternative?

the tolerance part would be the lines with jumpAllowTime, jumpAllowTimeTrack, waitToLand and waitToLandTrack

 void Start()
     {
         player = GetComponent<CharacterController> ();
         transform.position = spawnPoint.transform.position;
 
         jumpSpeed = Mathf.Sqrt (2 * gravity * jumpHeight);
         verticalSpeed = -gravity;
         jumpAllowTimeTrack = jumpAllowTime;
         movementSmoothFactor = groundSmoothFactor;
     }
 
     void Update(){
         moveHorizontal = 0;
         moveDepth = 0;
         moveSpeed = 1.0f;
         moveSpeedAir = 0.6f;
 
         //input
         onGroundInput = new Vector3 (moveHorizontal,0,moveDepth);
         //normalizes the vector so that diagonal movement doesn't get too fast
         if (onGroundInput.magnitude > 1) {
             onGroundInput.Normalize();
         }
         targetGroundMovement = onGroundInput;
         //lets the character walk into the direction the camera is facing
         targetGroundMovement = playerCamera.transform.TransformDirection (targetGroundMovement);
         targetGroundMovement.y = 0;
         targetGroundMovement *= onGroundInput.magnitude;
 
         //gravity
         if (player.isGrounded) {
             movementSmoothFactor = groundSmoothFactor;
             jumpAllowTimeTrack = jumpAllowTime;
             waitToLandTrack -= Time.deltaTime;
             debugText.text = "grounded";
         }
 
         if (!player.isGrounded) {
             movementSmoothFactor = airSmoothFactor;
             verticalSpeed += Physics.gravity.y * Time.deltaTime;
             jumpAllowTimeTrack -= Time.deltaTime;
             waitToLandTrack = waitToLand;
             debugText.text = "not grounded";
         }
 
         if (waitToLandTrack < 0.0f) {
             verticalSpeed = -0.1f;
             jumpText.text ="not jumping";
         }
 
         //jumping
         if ((jumpAllowTimeTrack > 0.0f) && (Input.GetKeyDown(KeyCode.Space))) {
             verticalSpeed = jumpSpeed;
             jumpText.text ="jumping";
         }
     }
 
     void FixedUpdate () {
         /*currentMovement converges to targetGroundMovement with time 
         currentMovementVelocity gets processed on every function call*/
         currentMovement = Vector3.SmoothDamp (currentMovement, targetGroundMovement * speed, ref currentMovementVelocity, movementSmoothFactor);
         currentMovement.y = verticalSpeed;
         player.Move(currentMovement * Time.deltaTime );
     }