This is def not your fault, you have made attempts multiple times to reach out to them, you listen when they talk to you, you seem like you genuinely care about her and her wellbeing. You saying her parents are going throu a divorce, not just a divorce but a rough one, she goes to therapy and that she's stressed. Due to all those stressors in her life could be the reason why she's been quiet, she may not know how to handle all that at once. Factors like that could lead to depressive/down/stressed behaviour. People being quiet and unresponsive to others is a common thing when someone is going throu it in life, it's draining, mentally and possibly emotionally. Online stuff serves as a distraction to stress. And as much as we want to help, we can't choose who the other person confides in, IF she is confiding to the other person. If she just has casual conversation with the other friend that that shows even more that they do make an effort to remain friends with you, even if it seems like it's only to vent.
I would say keep being persistent with talking to them. One of the last things that someone who is down needs is to loose a friend or someone to talk to. Loosing someone close to them just makes things worse. They will see that you've made the effort to talk multiple times, and hopefully when it'll all become much less stressful and more smooth. Once it does, they will see all those texts and know you do care for them. If you feel up to it, try to prompt them into talking about how they're feeling and tell them 'hey I know things suck now but you should know I care about you and you can tell me anything, I'll be here to listen'. Let them really know.
It is def not your fault.
Yes, she is seeing several doctors, and she also has had previous health issues, which doesn't help matters. It's very frustrating as none of these doctors seem to know what's wrong despite many tests and everything they try to help her, doesn't 
