Unless big changes to the environment happen at least once every generation, then there is no way that diversity of offspring will be selected for. Say you have a population of 100,000 organisms and 1 randomly mutates to produce more diverse offspring. That gives the gene a 0.001% occurrence in the population. Hardy-Weinberg principle says that gene will remain at about that percent of the population unless it is selected for. So if a generation passes without selection for that trait, there is a very high probability that gene's occurrence drops back to 0%.

In other words, without a constant source of selection, there is no way for a trait to become fixed in a population.