Could it not be that the lifespan is just significantly longer than the observation period? If we looked at human mortality in a sample of a few thousand individuals over the first 30 years of life it would also appear rather flat.
Example in context:
". Right-censorship
was applied in three cases: if the animal was (1) transferred to another collection, with the date of
transfer considered as the censorship event; (2) euthanized for research purposes when still healthy,
with the date of sacrifice as the censorship event; or (3) still alive when the process of compiling
records was completed, with the date of completion as the censorship event (see Materials and
methods)."
The authors address this this to some degree in the Discussion. See the para beginning "Indeed, naked mole-rat mortality was less consistent with a typical Gompertz model of hazard than it was with an exponential decay model, with a constant probability of decay (death) defining a species’ half-life."
The same things that make them die at three years old. The point is the rate of those things which kill, does not increase as much with age as it does with the rest of us mammals.
What makes them die younger is the real question. Their curve is pretty flat as a trend line (although with plenty of peaks and valleys) and seems to start at 600 day old mouse mortality rates. Although they are also infamously inbred.
I wonder if it would be possible to breed for lifespan by breeding only the 'elders' among them or if it would do about as much good as breeding for resistance to gunshots - outside circumstances not influencible.
Of course you can breed for resistance to gunshots.
Size, hardened skin, extreme speed of ducking reflex, regenerative capacity, spiderlike weaving ability etc. etc.
It works on fruit flies, see Rose, M. Laboratory Evolution of Postponed Senescence in Drosophila melanogaster. Evolution (1984), where the lifespan was doubled.
So this certainly works in principle. For longer lived species I expect it will still work, but it would take hundreds to thousands of years to breed for even a few dozen generations.
I would be concerned with secondary effects of aging on viability of gametes and chances of exotic conditions - doing this over any large span of generations would probably (temporarily?) yield a much higher mortality rate until we figured out the best ratio of increased parent lifespan to increased child mortality.
With humans you probably wouldn't want to wait with the breeding until the parents are old, but select breeding pairs based on the longevity of their (great-)grandparents. At least until you figure out useful biomarkers that reliably predict longevity already at the age of twenty or so.