Please help - Possibly dying cat

Our cat is about 10 years old. More than a year ago, she had a serious bout with kidney disease and had to be in the hospital for five days with an IV. When she came home, it took her about two weeks to get back to normal, but she did bounce back (used up yet another one of her lives!) and was fine until last month. She stopped eating and lost weight. We took her to the vet again, and we had to rush her to the hospital. After testing, turns out she had a kidney infection, not a repeat of the chronic kidney disease. But this time she had to stay in the hospital 10 days with the IV. Her test results dropped to normal and she came home, although she had picked up a respiratory disease in the hospital. She was a little off, like she was last time, but she has now been home three weeks and she's getting worse. She drinks plenty of water, but won't eat at all and she's practically skin and bones. I've tried every trick to get her to eat; sometimes she'll take a lick of tuna from my fingers, but that's it. I think it's because she can't smell. Her nose is still dry. She fights and struggles mightly every time we try to give her the anitbiotic and medicine for the respiratory illness. She absolutely hates it. She's taken pills before with not nearly as much trouble. OK, that's taken up way more of your time than I meant to take. The whole point here is that I can't see making her suffer more by taking her back to the hospital and going through all the blood draws (her veins are so thin they have to stick her several times to get what the blood they need) and being stuck in a cage with an IV for days on end (she's mostly an indoor cat, but she likes to take a tour of her domain outside once or twice a day). My husband had cats all during his childhood and well into adulthood; I was not a cat person, but this one was a stray who just moved in with us when she was barely a year old despite my efforts to keep her at bay. As is the way of the world, we are now very close (I think she thinks I'm just a strange-shaped cat) and I've never lost a cat before. She still walks around some and will even find the energy to jump on the sofa or bed maybe once or twice a day, but she rarely purrs now. Sorry, back to the question: How long can a cat go without eating? What are the stages of death? How do you know when it's near the end? What do I do?