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Pete Zourasof surviving each additional year once you turn age 99. As more people make it to that age, for the reasons you state, the population of people surviving past it will grow as well. If America has 100,000 people age 99, we can predict that 49 will make it to 110 (so-called "super-centenarians"). That number grows proportionate to the number of people starting at age 99.
The number of infant deaths of US males born in 1905 was 12,792 (for every 100,000 births). Infant deaths of US males born in 1935 was 5,848. US males born in 1997 died at a rate of 795 (per 100,000). Clearly surviving birth for people born in 1905 was no mean feat.