Hi. I'm in a long distance and i'm engaged as well. My fiance is very busy with work and I definitely have to understand he is that way. Whenever we're on the phone at nite and he has to get up early the next day, he simply says "baby, you know I have an early day tomorrow, I should get going, I will call you on break time tomorrow" and no matter how difficult it is for me to let him go, I have to do it, I have to understand him and I have to think about whats best for him. I strongly believe that all relationships have to be built upon communication, ppl are supposed to talk about whats bothering them so both can work things out finding a middle point where neither you nor her lose. Tell her gently whats going on with you, how the lack of sleep is affecting you, maybe you can schedule to call her earlier or you can make it up by giving her a quick call during the day and then one at nite, or send her an email as well. If she loves you, she will definitely have to understand you, and she has to seek for your wellness. Good luck!

Seldom am I judgemental of people, but I gotta say, your girlfriend is being downright selfish. She's showing that she doesn't care at all about your needs, and more than anything that her needs take prescedence over yours no matter what. If she's so utterly emotional about you denying her needs, no matter what the detriment to yours, that cannot be classified as anything short of extremely selfish. Sorry to be harsh, but I think you need to tell her that.