Several organisms, including humans, display a deceleration in mortality rates at advanced ages. This mortality deceleration is sufficiently rapid to allow late-life mortality to plateau in old age in several species, causing the apparent cessation of biological ageing. Here, it is shown that late-life mortality deceleration (LLMD) and late-life plateaus are caused by common demographic errors. Age estimation and cohort blending errors introduced at rates below 1 in 10,000 are sufficient to cause LLMD and plateaus. In humans, observed error rates of birth and death registration predict the magnitude of LLMD. Correction for these sources of demographic error using a mixed linear model eliminates LLMD and late-life mortality plateaus (LLMPs) without recourse to biological or evolutionary models. These results suggest models developed to explain LLMD have been fitted to an error distribution, that ageing does not slow or stop during old age in humans, and that there is a finite limit to human longevity.