Telomere shortening has emerged as an important biomarker of aging. Longitudinal studies consistently find that, although telomere length shortens over time on average, there is a subset of individuals for whom telomere length is observed to increase. This apparent lengthening could either be a genuine biological phenomenon, or simply due to measurement and sampling error. Simons, Stulp and Nakagawa [Biogerontology 15: 99-103, 2014] recently proposed a statistical test for detecting when the amount of apparent lengthening in a dataset exceeds that which should be expected due to error, and thus indicating that genuine elongation may be operative in some individuals. The test is however based on a restrictive assumption, namely that each individuals true rate of telomere change is constant over time. This assumption is unrealistic, since stress and life events are thought to affect telomere dynamics, and such events occur episodically. Here we show, using simulated data that realistically mirrors empirically-observed telomere parameters, that when the assumption of a constant true rate for each individual does not hold, the test fails to detect true lengthening in a wide range of cases where it does exist. The test also suffers low power under empirically plausible magnitudes of measurement error and likely lengths of follow-up, even when the constant-rate assumption is true. Thus, whilst a significant result of the proposed test is likely to indicate that true lengthening is present in a data set, a non-significant result does not mean that true lengthening is absent.