In male broad-horned flour beetles, Gnatocerus cornutus, losers of conflicts avoid fighting at subsequent encounters. The loser effect lasts for 4 days. It is considered that the memory of losing remains for 4 days. The duration of the memory is expected to affect the fitness, and the duration, 4 days, is expected to be optimal. We consider the fitness of a mutant in an homogeneous population to obtain the optimal duration. Here we carry out simulations using an individual-based model. The results suggest that the trade-off of getting mating chances and avoiding damage can cause the optimal duration of the memory, and that the decay in time of the female population is an important factor.