During SARS i remember reading its usually the opposite, a virus that kills its infected host too quickly ends up extinct by its own hand because it doesnt get as much of a chance to spread to an uninfected host, so over time most viruses mutate to have less virulence and become less deadly because the deadly strains die off while the others live on by giving their hosts just mild symptoms.
That's a reasonable argument. Just change JC's theory a bit and go with "the longer it sticks around and more people it infects, the more likely that an additional viable strain gets cooking and we start again at the beginning".