An online petition is certainly the most original approach I've seen to asking a partner to get back together.

After having read that you were disloyal to her on two occasions, I can understand her viewpoint that you're not trustworthy and frankly, I agree with it. If all it will take for her to give you another chance is two signatures on the petition, you already have what you need. If it were me in her position, the separation would be permanent.