"Never give up" isn't a motto you find on inspirational posters. It's the guiding principle of A Little Princess. Sara lives by these words as she endures one misery after another on her descent into poverty and fall from the esteem of Miss Minchin & Co. Even though her life is admittedly pretty terrible, Sara doesn't wallow in her sadness. She keeps her spirits up by making up stories and fantasies for herself, and keeps hoping that one day things will be better. She even does her chores without complaining. And that's more than we can say for ourselves.
Sara's unusual self-discipline helps her keep going even when things seem utterly hopeless.
Mr. Carrisford keeps looking for Sara even though he's ill and possibly at death's door because of his overwhelming guilt and loyalty to his friend.