... in fruit flies at least.
Tom A.R. Price et al, Polyandry Prevents Extinction. Current Biology, 2010.
There's also an article at Science Daily.
There seems to be a sex-ratio distortion (SR) X chromosome among some males that kills all the Y chromosome sperm before it can fertilize the egg, hence tending to produce an all-female offspring. By mating with various males, females prevent that this SR chromosome can become dominant up to the point of becoming a female-only population bound to extinction.
From the paper:
SR is a naturally occurring X chromosome meiotic driver that kills the Y chromosome-bearing sperm of male carriers [9,17]. SR therefore results in all-female broods and is inherited by all of the offspring of females that mate with male carriers [18,19]. This transmission advantage allows SR to spread through populations. However, the loss of half of the sperm produced by SR carriers makes them poor sperm competitors, with SR males...
Fruit fly populations in which females were forced by researchers (who acted as some sort of religious police, like in Saudi Arabia) to mate only with one male each, ended up after just 15 generations too crowded with this SR chromosome and five out of twelve (almost 50%) went extinct. Instead the control populations where free mating was allowed, remained healthy and kept the SR chromosome under control.
This seems to have implications beyond Drosophila pseudoobscura, the species used in this research, because both the "selfish" SR chromosome and the existence of promiscuity seem to be widespread through the animal kingdom.
It is quite curious how selfish genes, or in this case full chromosomes, do seem to exist but nevertheless they are not advantageous to their carriers. It is also curious how a mere drive in favor of diversity, such as promiscuity, helps to keep such genetic nuisances under control.