Having problems with GetButtonDown missing button presses

Here's the code I have on the doors in my level with each door containing a collision trigger:

 function Update () {
     if(Input.GetButtonDown("Fire1"))
         doorButtonPressed=true;
     else
         doorButtonPressed=false;
 }
 
 function OnTriggerEnter (collisionInfo: Collider)
  {    
     if (collisionInfo.tag == "Player")
     {
             doorPromptRef.renderer.enabled = true;
             doorPromptText.text = "[X] ENTER";
     }
 }
 
 function OnTriggerStay (collisionInfo: Collider)
  {
         if (collisionInfo.tag == "Player")
         {
             if(doorButtonPressed)
             {
                 GoToRoom();
             }
         }
 }

This works 90% of the time, but occasionally it will miss a button press (I test by rapidly going back and fourth between two doors).

I suspect this is occurring because Unity Script reference states "OnTriggerStay is called almost all the frames for every Collider other that is touching the trigger." But I don't know of a more proper way to go about handling this and don't want to make a hacky workaround yet.

I humored changing GetButtonDown to just GetButton, but if the player holds down the button they will warp back and fourth between doors too rapidly.

On a random side note that may or may not be relevant: I'm using ex2D.