Final answer:
In the given excerpt from 'A Worn Path,' the most likely meaning of 'obstinate' is 'stubborn.' The nurse describes the patient's case as being challenging or difficult to deal with.
Step-by-step explanation:
The most likely meaning of 'obstinate' in the given excerpt is 'stubborn' or 'difficult to deal with.' In this context, the nurse is referring to the patient's case as being challenging or resistant to treatment. The doctor mentions that it is an obstinate case because the patient's condition is recurring and does not easily improve despite their efforts to provide soothing medicine.