Even for a deaf, demented elderly man, incapable of doing any mitzvot, we must violate the Shabbat to save his life.
A treatment that will not reverse the condition to which it is being applied, even if successful, is an example of true medical futility.
Performing CPR on a terminally ill patient whose heart has stopped -- not because of a cardiac abnormality, but because the patient has reached the point at which his body can no longer support life -- is truly futile and may be withheld.
From a Jewish perspective, we must ask whether the physician may withhold, and whether the patient may refuse, futile therapy.
The intrinsic value of life does not necessarily imply that every patient must be treated in every instance.
The Torah teaches us that every moment of life is intrinsically valuable; life itself is never futile.
Rabbi Shlomo Zalman Auerbach, a leading halachic authority of the past generation, points out that we have no "yardstick" by which to measure value of life.
Practically speaking, this means that when a patient is approaching death, one may not take his temperature, measure his pulse or blood pressure, and certainly may not draw his blood unless curative therapy or comfort measures will be applied based on the test results.
A second form of futile therapy involves a treatment that is extremely unlikely to be successful, but is intended to reverse the condition to which it is being applied.
Her impairment is cognitive and Judaism does not recognize any less of a right to treatment for one cognitively impaired than one mentally astute.