As far as I can tell, the paper I linked to in my earlier post disagrees with you, Steamking.
From the paper:
A fundamental conclusion we draw from this analysis is that extensive longevity appears to be a novel feature of Homo sapiens. Our results contradict Vallois’s (1961: 222) claim that among early humans, “few individuals passed forty years, and it is only quite exceptionally that any passed fifty,” and the more traditional Hobbesian view of a nasty, brutish, and short human life (see also King and Jukes 1969; Weiss 1981). The data show that modal adult life span is 68–78 years, and that it was not uncommon for individuals to reach these ages, suggesting that inferences based on paleodemographic reconstruction are unreliable.
They're talking about pre-agricultural societies, which is exactly what the OP was asking about.
Most of which is irrelevant for bands of early human, as their small population size and low population density doesn't support the development of epidemic diseases and also helps inhibit their spread as far as I understand. Indeed it is actually contact with agricultural societies that commonly results in catastrophic epidemics. While disease is absolutely a primary cause of death among hunter-gatherers, to the best of my knowledge these are not epidemic diseases. Indeed the paper itself appears to support this:
Infectious disease is unlikely to reach epidemic proportions in small, isolated populations (Black 1975). In our sample, widespread lethal infectious disease was most common in groups that had been interacting with large populations of outsiders.
Interestingly, you can find an analysis of mortality rates for several hunter-gatherer populations during pre-contact and post-contact with developed societies in the paper as well.
The average age is low because mortality during infancy and childhood is so high. Again from the paper:
In Table 2, we see that on average 57 percent, 64 percent, and 67 percent of children born survive to age 15 years among hunter-gatherers, forager-horticulturalists, and acculturated hunter-gatherers. Of those who reach age 15, 64 percent of traditional hunter-gatherers and 61 percent of forager-horticulturalists reach age 45.
43% of studied hunter-gatherers died before the age of 15, but if you live to that age then you have better odds of surviving to 45 than you do of landing on black during a game of roulette. So while an individual may have had less than a 50% chance of making it to age 45, it was by no means a rarity and not something I'd call "small odds".