Wrong conclusion. It's over when you give up, but not before. Divorce does not make it over, your decision to stop trying is what ends it, and that's up to you.
Giving space is not the same as giving up.
She knows you want to reconcile, she knows you're willing to put effort into changing. You have delivered the message. Now it's in her hands and not yours.
Work on changes FOR YOU. Assuming this doesn't work out, you will have new relationships in the future. How can you be the best relationship partner you can be? How can you address the long term patterns that plagued your marriage? Dig deeply for your own sake.
Focus on that and have no expectations of a quick reaction from W. If you do it well, W will react, but not on your timeline.
You read "Divorce Busting" and/or "The Divorce Remedy" right? I also recommend you read "The Sex Starved Marriage" and "The 5 Love Languages", those should be required reading for everyone.
WRT giving space, your W wants emotional distance right now. Pretend she's drawn a 10 foot perimeter around herself emotionally. When you pursue her, you decrease that distance. She doesn't want you any closer, so for every foot you move in, she needs to move even farther away from you to maintain her 10 feet.
What happens when you move in the opposite direction, or give her even more space then she wants? If you increase the emotional space to 15 feet by moving 5 feet away, then she can safely move 5 feet back toward you without violating her limit. You've made it safe for her to approach YOU.
Back off and provide space, and you will see this happen, but it may take quite a long time. You will have to be more patient than you think you can be, but it's really the only thing you can do that's going to work. Anything else is guaranteed to fail, as you've been finding.
When she does approach you, or reach out, you must NOT come running back in. She's afraid that you'll do the equivalent of a running tackle and assume everything is now OK. You must never escalate above what she offers. If she hugs you, you can hug her back but don't kiss her or say "I love you" etc. All you can do is mirror.
Expect her to run hot and cold. She may "try on" being nice to you, and then will seemingly instantly turn cold and distant again. This is normal. She will catch herself being nice and won't want you to think everything is OK.
You're far from done if you want to keep trying. You need only to alter your approach.
Accuray
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015