Yes and no. The largest advances in life expectancy were in solving child mortality issues. In other words, when you hear things like "2000 years ago, the life expectancy was 25 years old", those averages are highly skewed by the large number of people who didn't make it to their 10th birthday. Meanwhile those who *did* make it that far tended to live not much less long than we do now.
In other words, for most of human history, once you hit a certain point you were about as likely to live as long as any other point. Obviously not considering outlier circumstances like periods of war or novel disease.
It's only been in recent decades where we're really starting to push beyond that, at least in the most developed of nations. This is due to growing ability to solve the issues that arise from living too long.
I completely agree with the initial part of your post. Childhood mortality reductions explain nearly all of the dramatic increases in life expectancy over time, and also is one of the best examples of how averages mislead. Some people have this impression of the past where people somehow just dropped dead at e.g. age 40 when in reality it was more like half were dropping dead before 10 and half were dropping dead after 70 resulting in an average age of mortality of around 40.
But I'm not sure I'm aware of any evidence for the latter part. Max life expectancy doesn't seem to be changing much at all, even over millennia (though obviously claims from long ago are impossible to objectively verify). This is far from an exhaustive search but the first thing that came to mind was to search for the longest lived people. [1] Of the 100 oldest women and 100 oldest men to have ever lived, only 4 of each are still alive today, and the most common nationality (and in fact the only nationality with more than 1 represented) is Brazil with 2 of the oldest men and 1 of the oldest women.
If we were pushing the bounds max life expectancy, then you'd generally expect to see a significant number of people breaking those records and - accordingly - still alive. In many ways it's kind of surprising that we're not even if we weren't making progress, since the total sample size of 'verified' peoples is increasing dramatically over time, so more people should be living longer (even if there is no change in max life expectancy) by chance/outlierdome alone. This to me is suggestive that we indeed be going in the opposite direction, though that's some extremely weak evidence of course.
The thing to look at is the shift of life expectancy at an older age, e.g. 65, and how that shifts over time. For instance: the UN has a dataset [1] demonstrating an improvement from roughly 12 years to roughly 16 years (i.e. total age 77 to 81) from 1950 to 2010.
Ah perhaps I misunderstood you. You're arguing that more people are reaching our 'expiration date' rather than that date meaningfully changing. That definitely seems true, but I think there's some very clear causal factors in play there (which that article doesn't hit on). Both smoking and drinking are on the decline which is going to send life expectancy at older ages way up.
And the various observations the article does make have similarly straight forward explanations. For instance gains have not been seen to the same degree in Eastern Europe where alcoholism, especially in the windows of time considered, was chronic. It also mentions dramatic gains in Asia but yet again you had things like China's Great Leap Forward and the Indonesian Genocide in the time frame studied where you were seeing deaths by the tens of millions. It's akin to saying that global life expectancy increased dramatically after 1945, which is certainly true.
In other words, for most of human history, once you hit a certain point you were about as likely to live as long as any other point. Obviously not considering outlier circumstances like periods of war or novel disease.
It's only been in recent decades where we're really starting to push beyond that, at least in the most developed of nations. This is due to growing ability to solve the issues that arise from living too long.