Resources last longer : If you have a relatively slow growth in your population, chances are the resources of your ecosystem will also last longer.
Less Intrapopulation Competition: If your population has a relative abundance of resources, there's nothing for the members of the population to compete over. This, combined with the above, means that the individual would likely have a longer lifespan.
Ex. Think about what would happen if there was a herd of elephants (who generally have a low reproduction rate) that had all of Southern Africa to itself. There's plenty of resources, and therefore no reason for compete for anything. Hence, each individual elephant would likely live longer.
Repopulation after Epidemic: If you have a relatively slow rate of growth in your population, then it will be difficult for it to repopulate an environment, say after a disease killed off half of it. In acrid environments, this greatly decreases the population's chances of survival.
Interpopulation Competition: If another population enters your population's niche, there's going to be competition. If the other population has a greater rate of growth, chances are they would outcompete your population (there are other factors to take into account, of course, but this is a reasonably good guess).
Ex. Back to the elephant example -- if a huge outburst of malaria killed off a third of the herd, it would be very difficult for it to recover from that due to low population growth. Also, say a colony is established in the same area where the elephants live. Every day thousands of people pour into the colony, and consume resources that the elephants normally would. The elephant population cannot keep up with that, and would likely be outcompeted for resources in this scenario.
Hope that helped :)