Why is Mrs. Jones a static character in "Thank You M'am" by Langston Hughes?
The answer to your question is simply a matter of applying the definition of the term "static character" to the character of the older woman in Langston Hughes' short story.
The enotes guide to writing character analyses (see the link below for the full guide) defines "static character" in these terms: "A character is considered flat (or static) when he or she does not experience change of any kind, does not grow from beginning to end."
The young man in the story clearly experiences a change in his awareness. The old woman does not experience a change. She's kind, generous, compassionate, etc. from the beginning to the story's end.