ActionScript 3.0 :: Slowdown: Memory Isn't Freeing Up

I'm having a bit of trouble in a game application I'm building,I recently added a bit of code that makes the game more visually interesting. As you move your character around screen, it creates instances of the GFX_Dot class, which is tied to a small green dot.In the class file I have a timer which decreases the alpha of the dot until it hits zero, at which point I'd like it to delete itself. Here are the functions I've got in the GFX_Dot class:

//GFX_Dot class
public function GFX_Dot() {
randomize();[code]..........

The part at the end "delete this" is meant to delete reference to "this" and allow it's memory to be re-used, however upon running the program, it's clear that they must not be deleting themselves, because after half a minute of creating a new GFX_Dot every frame at 30 fps, the game begins to get very slow. Before adding these graphical elements the game ran snappy all the time, I'm almost certain it has to do with them not being deleted properly.