You need to look after yourself or you'll end up completely wiped out and that's not going to bode well for your health, your work or your relationship.
If you push things too far, especially if you are using things like caffeine or other things to try and help you keep awake, then your body will try to intervene. I don't think trying to force your body to accept the way things are now is going to work, as your body doesn't seem happy.
Try to focus on quality time. If he is a decent guy then he isn't going to want you to burn yourself out just so that you can speak every day. I know it's not the same but you could always record video messages for each other if you aren't able to speak live. If you are exhausted then you don't want to end up resenting staying up to talk or being ratty when you do speak.
So, firstly you need to let your body catch up, get some decent sleep and rest and then work out a more forgiving schedule.