Shortly after receiving a diagnosis of pneumonia on Friday, Hillary Clinton decided to limit the information to her family members and close aides, certain that the illness was not a crucial issue for voters and that it might be twisted and exploited by her opponents, several advisers and allies said on Monday.

To those she did inform, Mrs. Clinton was emphatic: She intended to “press on” with her campaign schedule, she said. Her confidants concluded that she did not want to be challenged over her preference to keep the pneumonia private and continue working.

Mrs. Clinton’s inner circle was mindful of both her guardedness and her expectation of loyalty once her mind is made up. And she was optimistic that she could recover over the weekend, when she had only two brief events on her schedule, said the advisers and allies, who insisted on anonymity to disclose private conversations.

But Mrs. Clinton’s penchant for privacy backfired. On Monday, her campaign scrambled to reassure voters about her health, a day after she grew visibly weak and was filmed being helped into a van: unsettling images that circulated widely and led her aides to disclose the pneumonia diagnosis two days after the fact.