Another common misperception about science, which is held even by many
social scientists, is that, both in our ancestral past and in many
developing nations today, people die at a much younger age than they
do in contemporary western industrialized nations. They assume that,
for example, the average life expectancy of 40 years means that most
adults die at or around the age of 40. Contrary to this
misconception, most adults, both in our ancestral past and in many
developing nations today, live to be about as old as people do in
western industrialized nations.
The article basically says that the life expectancy of adults was the same throughout history.
(Note: The original version of this question asked about infant mortality, not adult longevity. The question was changed several days after this answer was posted.)
According to Kelly RL. 1995. The foraging spectrum: diversity in hunter-gatherer lifeways. Washington, D.C.: Smithsonian Institution Press. and Hewlett BS. 1991. Demography and childcare in preindustrial societies. J Anthropol Res 47:1–37. (cited in White, A. A. (2014), Mortality, fertility, and the OY ratio in a model hunter–gatherer system. Am. J. Phys. Anthropol., 154: 222–231.) the infant mortality in hunter-gatherer groups is from 20-30%.
By comparison, the rate in the USA (which has a pretty abyssmal infant mortality rate for an industrialized country) is about 0.6%, roughly 30-50 times lower.
It's a matter of understanding how a mean is computed. You can read whole books from Nassim Nicholas Taleb (among others) like "fooled by randomness" or "black swan" to understand why those mean calculations are counter-intuitive for our mind.
Life expectancy is a mean of ages from birth to death. This means that lots of deaths during childhood lead to a lower mean. But it does not mean that once you reach adulthood, you will not live longer:
With a pool of four individuals, if we take their death age, and compute the mean (life expectancy) :
2y, 2y, 2y, 60y : 16.5 years
20y, 20y, 20y, 2y: 15.5 years
We cannot conclude much from those "life expectancy" numbers which are almost the same.
This is why there is also the "life expectancy at older age". For paleolithic era, with a life expectancy of 33, it is stated: if a child survived until age 15, then its life expectancy will be 54 years, not 33. (numbers taken from this following study, linked on the wikipedia "life expectancy" article)
We can conclude that with a life expectancy of 33 during paleolithic, most adults died around 54 years, and even some must have reached 70 or even 80.
But of course a lot more people now live longer than in paleolithic, but it does not mean that in paleolithic a few people couldn't live until 80.
So did adult live the same through history? No, they live longer today.
Did some adults throughout history lived as old as most adult now and a lot more years than their life expectancy at birth? Almost certainly yes, even in paleolithic, because life expectancy is only a mean.
Yes, child mortality is much higher in hunter-gatherer tribes and acounts for a large increase in life expectancy at birth, but life expectancy increased in industrialized countries even for adult age.
For example, in the United States only, life expectancy for males was 21 years at age of 50 in 1900, but it was 30 years at age of 50 in 2011. Link.
In 1900, the US was already an industrialized society, therefore the difference between adult life expectancy in industrialized countries and hunter-gatherers will be even greater.