I agree with the others that you do seem to be a really good friend. If she is doing it for attention, try planning a positive activity with her -- something she is very good at. If you can, maybe try inviting a few other friends along & make a point to give her compliments. If she responds to that, there is a decent chance that maybe she is just pretending to be depressed for attention. It's not fool-proof, but often it can be a good indicator.
If she still seems really down the whole time, then it might be time to recommend she see a professional counselor (at your school, if you have one, or in the community). Depression is not necessarily something you can just try to get better from. Some depression is caused by underlying medical conditions -- or in very rare instances, depression is a primary condition caused by a problem in brain chemistry. In those cases, saying that she is not trying to cheer up is like saying that someone with severe allergies is not trying to keep from sneezing. It requires finding the cause of the depression & then treating that condition, usually with medication.
Other people have depression caused mostly by something that upset them (though over time that can cause a chemical imbalance in the brain). For them, it's easier to overcome the depression but sometimes they need a trained professional to recommend certain techniques for their specific situation that the person can do to help him/herself feel better. Sometimes this group of people can also benefit from anti-depressant or anti-anxiety medications.
In any case, it is not your responsibility to help her overcome her depression. That is a really hard thing to do & needs to involve doctors and a trained counselor. You have done the right thing talking to your head of year. Maybe the head knows something about your friend that we can't know over the internet. If she's faking, she will be able to be cheered up. If she's just sad, she should be able to be cheered up. I only wanted to explain that people with Major Depression usually cannot cheer up because the chemicals in the brain that make all of us feel happy are in short supply in the brains of people who are really depressed. Doctors can help treat that by giving medication. Counselors can help people understand their condition & learn special ways of not feeling so low all the time. They teach people who are depressed how to function with their condition & how to help themselves feel a little bit better. Depending on the cause & how quickly the person starts treatment, sometimes the person can feel pretty happy a "normal" amount of the time; others will continue to struggle with depression for the rest of their lives, but they can learn to help themselves and behave more socially around friends.
I hope that helps. You are a really good friend. Even if you need to tell your friend that you need a break & suggest she gets help, you are still a really good friend. I know that having a friend like you really helped me with my issues. Unfortunately, I relied on that friend a bit too much & she started drinking a lot. Now I'm trying to help her. If I'd realized that would happen, I wouldn't have shared so many of my dark thoughts with her. So I agree with Jamie that if it's getting too overwhelming maybe try setting up certain dates when you will talk with your friend & stick to them. If you are always staying up late listening to her negative comments (even if she can't help them except by seeing a doctor), you are more likely to get sick or sad and then you won't be much help. So please do take care of yourself. It will still be helpful if you say you will talk to your friend each Saturday (or any other single day of the week). That will give you a chance to rest up & really listen to her. If she's feeling better & just wants to chat about school or boys or whatever, then you could talk to her more often. But do be careful about always listening to the negative things.