The contradiction between the long-term persistence of the chromosomal hotspots that initiate meiotic recombination and the self-destructive mechanism by which they act strongly suggests that our understanding of recombination is incomplete. This "hotspot paradox" has been reinforced by the finding that biased gene conversion also removes active hotspots from human sperm. To investigate the requirements for hotspot persistence, we developed a detailed computer simulation model of their activity and its evolutionary consequences. With this model, unopposed hotspot activity could drive strong hotspots from 50% representation to extinction within 70 generations. Although the crossing over that hotspots cause can increase population fitness, this benefit was always too small to slow the loss of hotspots. Hotspots could not be maintained by plausible rates of de novo mutation, nor by crossover interference, which alters the frequency and/or spacing of crossovers. Competition among hotspots for activity-limiting factors also did not prevent their extinction, although the rate of hotspot loss was slowed. Key factors were the probability that the initiating hotspot allele is destroyed and the nonmeiotic contributions hotspots make to fitness. Experimental investigation of these deserves high priority, because until the paradox is resolved all components of the mechanism are open to doubt.