Make sure you are only propagating in one direction. It's not the green line you should be worrying about, it's the tiny green line coming off the blue square.
If you have added a new stroke at frame 10 and then propagate for 40 frames, then you go back to frame 20 and add a new stroke the propagation line will disappear between 20 and 40 because the new stroke has to propagate again. This is why it's important to only go in one direction and watch every frame as you go.
If you get to frame 40 and you realize that you need to go back a few frames you can add a new stroke at frame forty but if you try and propagate backwards nothing will be generated. You must go in one direction only. While it is possible to propagate a frame at a time backwards I have found that it almost always works best to go forwards.
Also, make sure that your Range and Direction of automatic propagation is properly set.