You've had this friend for a long time, and suddenly she is giving you the cold shoulder...you don't know why. Should you (a) ask her point black, what's up? Or (b) give her some space and see if she comes around. If you choose the latter, you will simply stew, and the thoughts in your head will race. Coming up with different scenarios as to why your friendship is on the rocks will make you crazy. Instead, choose A. Talk it out!
But don't get all defensive, and don't assassinate her character either. Instead, start out by saying, "I know you're upset, and I just want to know what I did wrong." You may have done or said absolutely nothing! But if you go with the presumption that you have, it will put her in the driver's seat, and get her talking. And then, listen!
And what ever you do, don't interrupt. Let her finish her story, and then comment. But without the "I did not!" thrown in there. Remember, you want to make peace, not start another argument.
Probably, it was all some miscommunication. So put everything on the table. If you said something that offended her, own up to it and apologize. If you said something you really mean, say that you are sorry she took it that way, but you really meant it this way.
See where I'm going with this? Diplomacy goes a long way. But if this person is so unreasonable that no amount of dialogue will change that...it's time to bite the bullet, and end the friendship.