If your girlfriend broke up with you because she was not ready due to work, school and family getting in the way, you shouldn’t make the mistake of hanging on.
If she wants to stay close friends, this could be a very tricky situation for you.
Being that you are still emotionally attached to her and would much rather that she be your girlfriend, you may be unable to truly be a platonic friend to her at this current time.
Every time that you interact with her as a close friend, you will be hoping that she changes her mind and tells you that she is ready to be your girlfriend again.
This is never a good position to put yourself in.
Hence, it may be best to create some distance between you and her until you have allowed your emotional attachment to her to wear out.
By allowing yourself to let go of her emotionally, it will be easier for you to be her friend.
However, if you decide to remain close friends with her because you are hoping that she will change her mind and decide to become your girlfriend again, you would be undertaking a dangerous gamble that most likely won’t pay off.