Hi I'm Rosie one of the vets and I'd like to try and help you and your cat. I'm sorry to hear that she isn't well. To be honest, I am a little concerned about what you have said so far. The first thing is that cats really can't cope without eating for a couple of days. The smaller you are the less able you are to cope, and cats as a whole tend to be quite small. The main thing I worry about with her is dehydration - cats get into a cycle where they don't eat, get dehydrated, feel ill, and don't eat. It can turn into a horrible cycle. They can also get low blood sugar. Sometimes cats can get a liver disease purely by not eating - when they don't eat the body mobilizes the fat (if they have any) for energy and this can overwhelm and damage the liver.
As for possible causes - most of the time when cats refuse to eat it is a simple infection causing a temperature, which is easily sorted out. Sometimes in older cats it can mean that their kidneys
aren't doing too well, but I would have expected you to see her vomiting on and off for a while if this was the case. Sometimes they have an overactive thyroid which initially makes them eat and drink loads, and act kittenish, but can occasionally make them depressed as you are describing.
I think, to be honest, that you are past the point where you are able to help her at home. I think she really needs to see a vet - I would phone them, explain the situation, and they should see you. Here it is illegal to turn someone away if they have a genuine emergency. If your regular vets won't see her, find someone who will. It is entirely possible that she can be treated by having some intravenous fluids (going on a drip) and some medication. If I saw her at my clinic I would want to do a simple blood test to assess how she is doing internally, and then probably get her on some fluids and medication. You may need to go to an emergency vets, but I really think she needs to be seen. This may be something completely treatable.
I hope I've helped - and sorry that I think she needs to go to a clinic urgently. If you have any questions from this then just hit 'reply' and I will get them and get back to you. Otherwise please leave a positive rating.
Thank you, ***** ***** luck, Rosie.