Detecting when a 2D object passes a point on a consistent basis

I have some code to re-position my background sprite once it moves past a certain threshold, that looks like this:

     //Update runs once per frame
     private void FixedUpdate()
     {
         //Check if the difference along the x axis between the main 
          Camera and the position of the object this is attached to is greater 
         than groundHorizontalLength.
         if (transform.position.x < -groundHorizontalLength)
         {
             Debug.Log("Pos: " + transform.position.x + " Length: " + -
              groundHorizontalLength + " Time: " + Time.deltaTime);
 
             //If true, this means this object is no longer visible and we can 
             safely move it forward to be re-used.
             RepositionBackground();
         }
     }
 
     //Moves the object this script is attached to right in order to create 
     our looping background effect.
     private void RepositionBackground()
     {
         //Move this object from it's position offscreen, behind the player, to 
         the new position off-camera in front of the player.
         transform.position = (Vector2)transform.position + groundOffSet;
     }

I've noticed that the condition gets met when the object is in slightly different positions each time (~0.1 on the X axis), which sometimes ends up leaving an unwanted gap between my two sprites.

Is there a way I can make the condition trigger on a more consistent basis, or an alternative way of triggering the re-position?