My suspicion is that it may have something to do with how the sprite is rendered. If the AnimatedSprite is always loading the same frames for each play-through, it could be that they are being re-indexed instead of re-rendered each time. This could result in them not being rendered to the same size, which could cause a slight blurring effect.
You could try to force a refresh of the given AnimatedSprite by calling it's _process() and/or _draw() functions. You could also try re-importing the sprites using the Godot pixel art import settings to ensure they are being rendered properly.
Another way to ensure that the sprites are being rendered properly is to use a ShaderMaterial instead of an AnimatedSprite. A ShaderMaterial allows you to specify exactly how the sprites are to be rendered, from scale to filtering, to giving them a pixelated look. If you're using Godot 3.1, you can use the Pixelate shader to achieve the desired look.
I hope this helps!
