The answer to this question can be found in Chapter Three, when Henrietta is called in for treatment after being told that her cancer is malignant. Even though it is clear she would have understood this was serious, she chose not to reveal what was really going on with her even with her closest family members. Note how the book explains this action:
Henrietta didn't tell anyone what Jones said, and no one asked. She simply went on with her day as if nothing had happened, which was just like her--no sense upsetting anyone over something she could deal with herself.
Even when she gets her husband to take her to hospital, she says that there is "nothing wrong" with her and the doctor is going to make her better. This refusal to tell others about her health clearly indicates the strength of Henrietta's character. She is not going to let others suffer for something that affects her alone. She comes across through this decision as a very stoical, resolute and determined woman.