The practice of infanticide by unrelated males has already influenced human evolution. Embryonic diapause can be part of a female's defense against having her offspring get killed by unrelated males.
Embryonic diapause facilitates early pregnancy termination. Early pregnancy termination prevents wasting resources on offspring that will be killed by unfamiliar males.
Sometimes a male will show up who wants to mate with a mother. Killing her pups improves the chance that she will become pregnant with those of the new male. The male's fitness is improved at the expense of the female, who has wasted resources on the prior pregnancy. This happens in lots of different mammal types. In mice, one function of embryonal diapause is to facilitate the Bruce effect - termination of a pregnancy when a new male is detected in the region.
The Bruce effect, or pregnancy block, is the tendency for female
rodents to terminate their pregnancies following exposure to the scent
of an unfamiliar male. The effect was first noted in 1959 by Hilda
M. Bruce, and has primarily been studied in laboratory mice (Mus
musculus). In mice, pregnancy can only be terminated prior to
embryo implantation...In many rodent species, males kill unrelated
young; pregnancy block may avoid the wasted investment of gestating
offspring likely to be killed at birth. The Bruce effect is
most common in polygynous rodent species, for which the risk of
infanticide is highest.
A new male will probably kill any pups not his, so no reason to carry them to term. Recycle those resources and start fresh.
Infanticide by strange males is still a major cause for infant mortality in humans - stepdads and new boyfriends are dangerous to infants and young children. There is reason to believe that regular infanticide by strange males has driven human evolution: the ability for females to have sex at any time in their cycle, concealed ovulation and breasts that always simulate lactating breasts are all parts of the human phenotype evolved to confuse potentially infanticidal males as to the reproductive state of a given female. If it is possible an infant might be his, he should not kill it. This benefits the fitness of the female at the expense of that of the male, who will waste his efforts and resources protecting offspring that is not his.
A Bruce Effect type phenomenon in humans could have easily been produced by these same selective pressures, as it was in mice. It could even have been produced in tandem with the above - the Bruce effect works on embryos in diapause but not once a pregnancy is underway. A human might keep a pregnancy in diapause if it were conceived under iffy circumstances with a questionable father. Perhaps the father would need to stay present in the vicinity for some time before the pregnancy would launch in earnest. Once underway, if the father disappeared and a new male arrived, tactics from the existing human repertoire would be used to confuse the issue of paternity such that the new male might think the newborn might be his, and so not kill it.