"That" cannot refer to people.
So we are left with ACs B,D and E.
(D) who in childhood might have at one time died
>>> implies the people actually died when they were children.
The SC means to say the people who might have died of these infections are now alive because of the medical blah blah.
(E)As a result of medical advances, many people who, when they were children, might at one time have died
of such infections as diphtheria, pneumonia, or rheumatic fever now live well into old age.
>>> I think this AC changes the meaning of the SC as well.
B is left.
This could very well be a IIlism question.
As a result of medical advances, many people who might once have died in childhood
of such infections as diphtheria, pneumonia, or rheumatic fever now live well into old age.
Hope this helps