A PNAS paper by Eileen Crimmins and Caleb Finch finds evidence that early infection, growth, and longevity are all linked:
ABSTRACT: Using historical data from cohorts born before the 20th century in four northern European countries, we show that increasing longevity and declining mortality in the elderly occurred among the same birth cohorts that experienced a reduction in mortality at younger ages. Concurrently, these cohorts also experienced increasing adult height. We hypothesize that both the decline in old-age mortality and the increase in height were promoted by the reduced burden of infections and inflammation. Thus, early growth and cardiovascular diseases of old age may share infectious and inflammatory causes rooted in the external environment.
The paper shows that, at least in the study populations, a reduction in early mortality not only affects the early part of the life table but actually flattens the mortality throughout the lifespan to some extent. Avoiding early infections appears to have cut old-age mortality at the same time it increased early growth.
I wonder to what extent the link between early infections and later inflammation and chronic disease is a product of recent disease evolution. It's not clear, since chronic inflammations were apparently common among some (and possibly all) archaic humans. But these probably did not bear any relationship to many of the epidemic diseases that have recently caused so much childhood mortality. On the other hand, there have been some very long-lasting ones -- tuberculosis comes to mind, as one that can have far-reaching infectious consequences in the body and has a long evolutionary association with humans.
Crimmins EM, Finch CE. 2006. Infection, inflammation, height, and longevity. Proc Nat Acad Sci USA Online before print. Abstract