Input.MouseButtonUp(0) sometimes not detected in Update() method

I have a simple shoot script that is called from a recorded input in the Update() method. I initially used if(Input.GetMouseButton(0)) as it is perfect for what I want, however, I noticed that sometimes, specifically when I click the mouse button several times fast, and in the end not be holding down the mouse, Input.GetMouseButton(0) will still return true. I wrote my own script that would perform the same task as Input.GetMouseButton(0) using mouseUp and mouseDown, however, the same...

Input.MouseButtonUp(0) sometimes not detected in Update() method