  We study how the Hurst exponent $\alpha$ depends on the fraction $f$ of the
total time $t$ remembered by non-Markovian random walkers that recall only the
distant past. We find that otherwise nonpersistent random walkers switch to
persistent behavior when inflicted with significant memory loss. Such memory
losses induce the probability density function of the walker's position to
undergo a transition from Gaussian to non-Gaussian. We interpret these findings
of persistence in terms of a breakdown of self-regulation mechanisms and
discuss their possible relevance to some of the burdensome behavioral and
psychological symptoms of Alzheimer's disease and other dementias.
