How long can someone live without food and only drinking water?

I am caring for my mother with ESLD. I spent 6 weeks in the hospital with her and was told she had days to live. I brought her home to hospice with family and though the first few weeks were rough it seems we are all finding a flow and enjoying each others company. My mother was a terrible alcoholic most of my life, but has finally quit drinking and I really cherish this time with her (She is 58). The nurses that visit talk about how much she has stabilized and almost seems to be doing better. I feel like she is doing better too, however she doesn’t eat. She drinks plenty of water and munches on ice but I haven’t seen her eat more than 100 calories in a day since August 12, usually in the form of diluted juice. Sometimes it is obvious she is hungry and tries to eat but will vomit or spit her food out after only a bite or two. I feel so sad to think she is starving to death but no one seems to have an answer beyond Ensure (which also makes her vomit). I cook her or buy her anything she asks for and she does not want an I.V.
I have to admit at first I wondered if it was ever going to end and now I have to hold back tears most parts of the day thinking that she won’t be around much longer. I am truly baffled at how well she is doing while only drinking water.