It depends. Is she in obvious pain? Is she "depressed" (in the veterinary sense, meaning that she is not showing interest in food or water, not showing much awareness of surroundings)? Do you feel that you have done everything that you can for her?
I think maybe the question is really more about you than about her. For some people, the first sign of illness is treated with the "hatchet method." These people reason that the chicken is not the same thing as a dog or a cat, but is a utility animal whose utility is at an end if veterinary (or even home veterinary) care is required. Other people will go to great lengths to keep their feathered companions alive and well, incurring large expenses or investments of time. Sometimes the response depends on the individual bird, but in general most people fall somewhere in between. You only need to ask yourself where you fall. There is no one right answer for everyone, or even for every chicken.
I would add though, that if you are planning on putting your hen down, the most humane way to do it is to actually put her down yourself, via the "hatchet method" or something similar (or have someone else do it for you), rather than leave her "for nature." I lost a few hens to this method my accident and I can assure you it was not a quick or easy death for them. Better to control how it happens so you can be sure it is humane, and you can have no regrets that you did the right thing, in the right way.
My thoughts are with you and your hen. And if it helps, in a home vet care situation with a chicken, if she is not going to make it but is not in obvious pain or discomfort, my personal choice is to continue the care and let her die on her own.
