In my opinion, you’re a very good and caring person! Also in my opinion, if there would be more people like you then there would be less people like your sister suffering from depression. She is very fortunate having you as a sister. Yeah, it’s a very good thing that you are staying in touch with her, she needs it. However, if she is depressed and she doesn’t want to help herself in the first place then I really doubt that you can have some control with that. I’m sure that she knows you care about her and surely she understands that you would be near her whenever she needs somebody nearby or just simply company. In the case if she would want or she would need to discuss more with you, then definitely she will let you know about that right away.
If I would be in your situation then I would send her letters from time to time, occasionally, not big ones, only telling her that you are thinking about her and you can tell her a short story about how are you doing in your life. That would be better than calling her or talking with her through skype and so on. She will read that letter alone where she can let her emotions go. It would be better… That’s because when people like your sister are depressed, majority of them are feeling somehow overwhelmed because they have to be around other people. As any other person, even non depressed, she has to show of some strength. Perhaps that is the reason… Maybe she doesn’t really have that strength. I’m not a doctor but I was in that situation few years ago, I was in a mild depression due to the exact same reason... I would recommend you not to do any drama about telling her how bad or how good life is, just try to keep things as light as you can.
Well, but if you think that there’s a possibility that she may be of some danger to herself, then that’s a completely something else. Other than professional help and hospitalization, I cannot recommend you, unfortunately. Moreover, your parents help here is essential. I wish you the best and good luck, I really hope your sister will get better as soon as possible.