It's likely a reference not to natural infant mortality, but to the apparent opposition to infanticide by early Christians. Rodney Stark in his seminal Rise of Christianity claims that this opposition made Christianity more attractive especially to women, since infanticide was legally a right that belonged only to the father.

Early Christian writings that support the view that early Christians opposed infanticide would be in the Didache (an early Jewish-Christian "handbook" for evangelists) which contained the injunction,

"You shall not murder a child by abortion nor kill that which is born." (Did. Ch. 2

and the Epistle of Barnabas which has a similar injunction:

Thou shalt not murder a child by abortion, nor again shalt thou kill it when it is born. Barnabas 19:5.

There were also some early Christian commentators who explicitly condemned infanticide such as Justin Martyr Apology XXVII so it's fairly well established that early Christians opposed infanticide and abortion possibly as early as the 1st Century. Stark says that this had a result of Christians basically out populating pagans in some areas just by virtue of not killing the girls (usually it was girls or deformed infants who got drowned or exposed).

Eventually, Constantine tried to limit infanticide by using imperial funds to assist poor families, widow and the like, offering financial rewards to those who kept children rather than killing them and offering public charity to churches (Robin Lane Fox, Pagans and Christians) and was finally banned altogether by the Emperor Valentinian.

So basically, it wasn't that Christians were less likely to have infants die of natural causes, but that they didn't practice infanticide and used both the government and the churches to condemn the practice, provide help to those in need, offered incentives not to do it and eventually banned it outright.