Welcome to the forum and thanks for reaching out.
Firstly, I am sorry it has taken a while, for you to get a reply, and this has nothing to do with you but it just something that happens .
You have written a very moving post about your relationship and I can see you are a very compassionate and caring person.
You understand the complex nature of the relationship and the problems your girlfriend faces.
Would you consider talking to a trained person on the Beyond blue support line 1300 224636
It is very difficult being with someone who is depressed and it is even more difficult being depressed and coping with your emotions. Some people do need space when they are depressed and time to work things out but I can understand how that would be very hard on you.
The more you pressure her to see her, the more it may upset her .
I realise it is very difficult for you but she seems to have insight into what she needs at the moment. You can offer her support and friendship at this time.
Would you consider contacting Beyoond Blue Support Service 1300224636which offers suppprt action and advice. sometimes talking through your problems to a trained person can help you sort out a few issues.
feel free to post here as much as you like. these are just my thoughts and you may not agree. thanks again for sharing your story.