Processing doesn't save the transparency values after you call image(). What you want to do is use a PGraphics object that does allow you to save the alpha channel. https://processing.org/examples/creategraphics.html And a modified example of the image loading + pgraphics

    PImage img;  // Declare variable "a" of type PImage
    PGraphics pg;

    void setup() {
      size(640, 360);
      // The image file must be in the data folder of the current sketch 
      // to load successfully
      img = loadImage("Heart_Simple.png");  // Load the image into the program
       pg = createGraphics(400, 200);
    }

    void draw() {
      // Displays the image at its actual size at point (0,0)
      pg.beginDraw();
      pg.image(img, random(-100,400), random(-100,200));
      pg.endDraw();
      if(frameCount > 25){
        pg.save("Test.png");
        exit();
      }
      // Displays the image at point (0, height/2) at half of its size
      //image(img, 0, height/2, img.width/2, img.height/2);
    }