IF you were to give it one last good shot, what's the approach?
But you're beating a dead horse. This thing now only exists in your mind. She's not there. She has left the building and you're still trying to figure out what door you should open in the building to find her standing there.
And should you leave the building and run up to wherever she is and say "hey! Let me let you know that I'm still interested in you, despite the fact that you don't return my calls and you didn't keep the dates with me and that you disappear on me" - what are you asking for, given her pattern, except for more of the same?
The ONLY important factor is the woman's interest in you. If it's not there, perseverance doesn't create it. You only become an annoyance. Perseverance only works in Romantic Comedies. In real life, the things these guys do in movies to persevere after their objects of affection would get them arrested for stalking and harassing. Perseverance is not the way to attract a woman.
Turn it around: What if there was a woman you dated a bit but then decided you didn't wish to be with, were not interested in, but she kept on pursuing you? You shrugged her off, didn't return her calls, disappeared, flaked on her, you're just NOT interested. Oh, you maybe entertain a phone call from her now and then and chat a little and share a passage from a book, because you think you're being nice and civil and pleasant (but it also sends her a mixed message that encourages her), BUT overall, you're not into her, you DON'T want to date her, and your actions show it... but she perseveres anyway. In fact, just the other day, she sent you a little note asking you if you wanted to go out to lunch or dinner. What would YOU think?
So, you went through a divorce and I guess your ex was the one that left the relationship. Have you figured out what part you played in her not loving you any more? That's rather important soul searching stuff, but necessary so as to make changes so that it doesn't happen again. Relationships are but shadows of the two people in them, so there's a part you played that needs to be looked at before you can get involved with someone new. Whether it's that you neglected her, abused her in some way, dominated her or became supplicant or just chose the wrong person, there's a part you played.
I'm also guessing that because the divorce is rather recent, there's an injury in your esteem, and having the very next gal dump you only serves to pain that still raw wound again. You may have to be alone for a while to really become your own person again and center yourself, learn, grow, heal and then, when you're ready, seek someone new. In the meantime, just relax, let go, have fun, find new hobbies to take up, passions to pursue, fill your life with things you've always wanted to do, meet other women, not for love, but just for laughs.