Regular observations by the All-Sky Monitor aboard the Rossi X-ray Timing Explorer satellite have yielded well-sampled light curves with a time baseline of over 10 years. We find that up to eight of the 16 brightest persistent low-mass X-ray binaries (LMXBs) show significant, possible sinusoidal, variations with periods of the order of 10 years. We speculate on its possible origin and prevalence in the population of LMXBs, and we find the presence of a third object in the system, or long-period variability intrinsic to the donor star, as being attractive origins for the X-ray flux modulation we detect. For some of the objects in which we do not detect a signal, there is substantial short-term variation which may hide modest modulation on long time-scales. Decade time-scale modulations may thus be even more common.