She hurts and then asks me to forgive, and again she repeats?

Long distance relationships are really hard. It sounds like a pattern has started with her and if you want to stay together you need to stop the pattern of hurt, sorry, hurt, sorry. Now exams are the most important thing so that must be priority, so send her some beautiful flowers or give her a promise ring, maybe she is just feeling insecure and having something she can show family and friends might solve this problem. Another thing to think about honestly, do you give her enough attention when your on the phone or emailing, do you really listen to her. Sounds as if she really misses you. Good luck