Well, you've asked her out three times in a row and she's said no for the same reason every time. What makes you think that response is necessarily going to change?
As for telling her to 'leave' C, I don't think that's the best of ideas. You're supposed to be friends with her remember? Think about how you'd feel if another one of your girl friends told you to break up with your girlfriend, and you knew that they liked you. You probably wouldn't take their suggestion seriously, and you know they have motives for the request...
However, it's good to see that you're still dating other people whilst crushing on this girl. :) But do you think those relationships are "regrets" because of your on going crush on A?
I seriously think you should just let her go. She's told you more than once that she wants to be friends. It might be hard, but you've got to accept it and move on with your life.
First off, it is absolutely not your place to tell her to leave the guy she is "semi-dating". This is her decision to make. It's none of your business unless she comes to you and asks for your advice.
It has to be said that the "I've been hurt and don't want to lose a friend" line probably really means that she doesn't like you as more than a friend, but doesn't want to come right out and say so to avoid hurting your feelings. Most likely she hasn't considered that it may also giving you false hope.
The reason you can't get over her is because the two of you are still hanging out together and she is giving you mixed messages. There may not be much you can do to discourage her flirting, so perhaps the best solution if you want to get over her is just to see less of her. And if when you are together she starts flirting, do what you can to discourage her - talk to someone else, find something else to do, leave the room even... If she asks what the problem is, tell her that her flirting with you while she's dating someone else makes you uncomfortable.
If she truly values you as a friend, or potentially something more (although in all honesty the latter seems a very slim possibility), then let her be the one to do the running in your relationship. You've told her often enough how you feel; she's definitely got the message. Currently she's probably secure in the knowledge that you're always waiting for her in the background like a devoted puppy. Let her lose that security and maybe she'll re-evaluate how she's been treating you.
Something very similar happened with me for the past two years and i had to break my friendship with this guy i adored because i couldn't stand having him so close and so far.
i believe you should at least try and move on. What you see as flirting can mean just friends caring for her.
Honestly, I would just give up. Or sit her down face to face, and flat out tell her that you really want to be with her, and that she needs to tell you if there is any hope at all of that ever happening. If she says no, move on. If she says yes, proceed with caution.
I do have to point out that just because she flirts, doesn't necessarily mean she's interested. I flirt with guys all the time, it's just how I get to know them. Granted, you two know each other fairly well by now, but she just sounds like a flirty person. I'm assuming she isn't flirting at the same magnitude she would be if she wanted to be with you.

There is probably a chance that she is confused also about whether or not to take the chance. On the negative side. if you do actually date her then end up breaking up you'll probably no longer talk to each other. I've seen it happen plenty of times. :(

First of all, the whole 'I don't want to lose a close friend' is the very first thing a woman who has a male friend interested in her is going to tell him if she just doesn't want to date him. It's a nice way of saying 'no, drop it'. That's not to say there aren't women who have male friends interested in them that they really don't want to date out of fear of losing them as friends, but this is generally a major alternative to 'leave the subject alone, I don't want to be with you, and I doubt I ever will'.
If she has shot you down three times with the same reason, it's true. Leave it alone. She doesn't want you. She wants a friend in you, and you seeing her flirting could just be you picking up on things you didn't notice before due to infatuation. Her 'flirting' could just be friendly gestures, or playful jokes. They're not necessarily a sign that she wants to date you. I 'flirt' with my male friends all the time, and they 'flirt' back, but neither of us like each other. Flirting doesn't always mean attraction.
Do not tell her to quit dating a person. That's a surefire way to put her on alert, watching for any signs of over-protectiveness or clingines in you, and to make her agitated at the same time. You do not want that, believe me. If she thinks you're getting obsessive, or you'll begin to keep careful watch over her lovelife and try to control it, then you'll lose her as a friend.
I'd say let it go. She obviously isn't interested, she's obviously made it clear, and you're obviously not getting her attention in a positive light. If she does like you, she'll let you know, rather than blowing you off by saying she doesn't want to lose a close friend. That phrase alone implies she does like you, when she's insisted she doesn't.
Honest Truth:
She has already turned you down three times. She does not want to date you.
I would not ask her again, at least not any time soon.
Girls usually all work in a similar way. So there are three possiblities here.
Number One: You guys have been so close for so long she does not think of you as a possible boyfrined. Almost more of a brother. She feels like you are best frineds and when you think she is flirting she is just treating you like a brother or a best frined. She is being open and not nervours/worried about what you will think because she thinks you are so close. She honstly does no want to date you and just wants too be your best frined. This could either be because you are so close she would feel like she is ruining a relationship or because she is not actually attracted too you. Maybe she thinks your personality is perfect but she does not have ANY attraction. Either way she flat out does not like you like that.
Number Two: Similar too number one but she is interested in you, however she thinks she is young and knows if you guys break up your relationship will be weird. Maybe you guys would stop being frined all together and she does not want too louse that. She knows you are in love with her and she probably feels pretty simliar towards you but she is not ready to settle down. She wants too date around, and have fun. She wants too date crazy guys she can party with or really hot ass hole guys.... or whoever it may be she just wants too have fun and she knows if she dates you she is going to want too settle down or will get bored of you at this point because she is not lookig for "the one" or a long term relationship right now. Or maybe she just wants too make sure you are the one before she throw her feelings too you.
Number Three: You are her backup. She knows you like her a lot and when she wants her self asteem boosted she comes too you. When she wants too feel loved she comes too you. She knows you care about her and she can always have you. She also knows no matter what you will be there. She does flirt with you, but it's not heartfelt she is just doing it too make her self feel better and keep you under finger. She want you too think you /might/ have a chance so you will continue too like her however she only thinks of you as a frined and thats all she will ever think. Unless you get her drunk after the love of her like breaks up with her then she might try too come on too you. Anway she pretty much thinks of you as a close frined and a self asteem booster. As soon as she finds "the one" or who she thinks is "the one" she will stop talking too you when she is around him and only talk too you when she is alone and bored, or feeling down comig back too you for again too boost her self asteem.
I can almost 100% promise she is in one of thoes situations and what ever it may be you should not try too make a move on her just wait and see how it goes. You will know when the moment is right. And obviously it's not right now because you are questioning it
ily