How to make image fade in and out in a loop?

Not sure what you're doing with x,y but as far as simply fading something in/out in a loop you should look at TweenLite/Max - it makes this quite simple:

fadeOut();

function fadeOut(){

          TweenMax.to(Hurt, 1, {alpha:0, onComplete:fadeIn});

}

function fadeIn(){

          TweenMax.to(Hurt, 1, {alpha:1, onComplete:fadeOut});

}

Or, you can even do it in one line:

TweenMax.to(Hurt, 1, {alpha:0, yoyo:true, repeat:-1});

// fadeInOutF should repeatedly execute (eg, using an enterframe loop):

var fadeIn:Boolean;

function fadeInOutF():void{  // add event to function argument if an enterframe loop is used

if(Hurt.y<0 && Hurt.x<0){ // not sure this part makes sense but it's part of your code so i added it.

if(fadeIn){

Hurt.alpha+=.03;

if(Hurt.alpha>=1){

fadeIn=false;

}

} else {

Hurt.alpha-=.03;

if(Hurt.alpha<=0){

fadeIn=true;

}

}

}

}