This paper studies the problem of controlling finite nondeterministic transition systems to satisfy constraints given as linear temporal logic properties. A controller architecture is proposed that maps finite fragments of the state trajectory history to control inputs. This approach avoids the standard controller construction that employs an onboard automaton which is fragile to memory loss or errors. In contrast, the proposed architecture requires storing only a finite sequence of previous system states in memory and is therefore resilient to memory loss. In particular, the system will operate unaltered after such a memory-loss event once the system recollects this finite sequence of system states. A generalised algorithm is outlined for controller synthesis in this manner. Additionally, we demonstrate the construction and implementation of such a memory-loss resilient controller through an experimental demonstration on a differential-drive robot that experiences memory-loss events.