When you think you have a good relationship, it can be hard to let it go. If you're hoping to get a second chance with an ex, how you ask for that chance can make all the difference in whether or not you get it. Keep desperation out of the picture in order to make your ex feel validated and wanted in a healthy way, and to show that you are capable of moving your relationship forward in a new and different manner.
Take some time away from communication with your ex. Not only will this give you an opportunity to look at the situation from the outside, it will show your ex that you're capable of being on your own, at least temporarily. Judge for yourself how much time is enough, but it should be longer than what your ex is likely to expect from you in “desperate” mode.
Address your anxious feelings. If you're worried about looking desperate, there's a good chance that you feel somewhat desperate about the possibility of this relationship ending. Bear with those anxious feelings and do your best to simply tolerate them and study them. Spend time with close friends and family to remind yourself that you have a support structure other than your relationship. Think hard about the complaints your ex has made about you and the relationship. Think about damaged trust and what you might have to do to repair trust or show that you are taking new action to break a cycle of bad behavior.
Ask your ex to speak to you about what's happened between you. Do not demand to have a conversation or act as if you are entitled to be heard.
Clear the air before bringing up the topic of trying again. Apologize for your mistakes and express understanding of the emotional effect they've had on your ex. Make it clear that you care about your ex's feelings and that this apology is unconditional.
Communicate your desire to revive the relationship as a statement, not a question. Do not press your ex for an answer immediately. Let him answer now or answer later.
Leave things open ended. If your ex is still adamant that the relationship is over, ask that she think about what you've said and let you know if she ever changes her mind.