third times a charm?

It depends on when things happen. If formal recruitment happens first, then the colonization, try it. But ask yourself what went wrong the last two times. Did you not engaged enough, not seem interested, were you shy? Etc. It's like a job interview, you have to be enthusiastic. Also, be prepared to answer why you didn't join before now, keeping in mind that some houses may remember you. Don't dwell on it. Say it didn't work out before but I really want to commit myself to a group and make a positive contribution. Remember that with some groups though, once cut = always cut. Be prepared to end up with the same result, or being cut completely though, if you go through with it. That could happen to a freshman too though.

If you decide to pursue formal recruitment and it doesn't work out, then maybe try for the Alpha Xi Delta colony. It's not a back-up plan, but it will possibly be a second chance. Don't expect a guaranteed bid, because they are particular about the members they want for their colonies and will likely cut a lot of girls who do go for the colony. It's usually get to know you events and then formal interviews. Remember to look nice and make a good impression. Colonies are usually more accepting of Juniors to mimic the existing structure of groups and pledge classes. If they took all freshman, the whole chapter would graduate at once. Know how you want to get involved because colonies often look to older women to assume leadership roles.

Good luck.

Why couldn't you see yourself in that final organization?

I'm also a Junior thinking about rushing for a third time and I was just wondering what goes through your mind, as a sister in an organization during formal recruitment, if someone says that they are a junior and this is their third time participating in formal recruitment. Is it negative, like if you haven't gotten a bid by now you aren't getting one, or is it more positive, like wow she is really dedicated and must really want to be in a sorority maybe I should give her a chance and see what that perseverance and dedication could bring to my organization....just wondering

It wasn't meant to be a harsh criticism, it was meant to be the honest answer you're looking for. Let me explain a little: Sororities know a lot can change with a person in a year, and they're going to reconsider you, but that doesn't mean they will offer you a bid just because they take another look at you as a PNM. If they for some reason have a negative impression of you, you're working against that and a negative opinion of a person is difficult to change, so you would have to really "wow" them if that's the case. If they just kind of forgot you and you didn't stand out, you have a chance to make more of an impression, and you want to make sure that you do this and that it's a good impression. If you view recruitment and go through with it the way you always have, you'll get the same results as before.
Please remember, that the same way a lot can change for an individual in a year, a lot can change for a sorority. So the same way you want them to consider you again and keep an open mind, do that for chapters you may have not given a second thought in the past. When you write off chapters that aren't your first (or second, or even third) choice the first day, they can tell. And then if you end up getting cut from your first choice, there may not be the opportunity to find where you belong because you basically blew off a chapter that would have given you a chance.

You have a good shot at axd because they need to take juniors and not many come out ! Def try it !!

Honestly sororities typically remember exactly who they chose not to extend a bid to the previous years, and unfortunately that impression tends to stick with the members of the organizations. So, if your first impression of the organization was negative and you were not invited back (twice), then that is likely to happen a third time. I think that you should give the final organization which gave you a chance a try and if not then join AXiD (yet no bids are guaranteed).