fade down, STOP. fade up, STOP.

I think you might be after this:

boolean compare = true; 
const int anPin = A5;
int ledPin = 9;    // LED connected to digital pin 9
int fadeValue;
void setup()  { 
  Serial.begin(9600); // nothing happens in setup 
  pinMode(anPin, INPUT);
  pinMode (ledPin, OUTPUT); // ADD THIS
} 

void loop()  { 
  int   avRead = analogRead(anPin);    //11-25 values
  Serial.println(avRead);
  delay(100);

  if(avRead > 15 && compare == true){ // fade up if avRead is >15 and fade down has run
    for (int fadeValue = 0 ; fadeValue <= 255; fadeValue +=5) { 
      analogWrite(ledPin, fadeValue);
      delay(30);
    }
    compare = false;  // set compare for fade down when avRead goes 15 or lower next pass thru loop
  }
  if (avRead<=15 && compare == false ){
    for (int fadeValue = 255 ; fadeValue >= 0; fadeValue -=5) {  
      analogWrite(ledPin, fadeValue);
      delay(30);
    }
    compare = true;
  }
} // end void loop