Just a couple of things:
First, dominant and recessive do not have anything to do with how common alleles are in a population. Polydactyly (extra digits) in humans is a dominant allele, but it is only found in a tiny percentage of the population. The recessive allele – that for only five digits per – is far more common. And genes do not “remain” recessive; they are either recessive to another allele or they are not. If they are, they will always remain so.
Also, all genes are not dominant/recessive systems. In fact, very few are. Widow’s peaks and attached earlobes are dominant/recessive traits in humans. Other gene systems have incomplete dominance. Snapdragons have red and white flower color alleles. Individuals with one of each have pink flowers: the red allele is incompletely dominant. Then there’s codominance where both alleles are dominant: i.e. if an individual has both of them, both are shown completely. Human MN blood groups are like this. If someone has both M and N allels, they express both M and N proteins on their blood cells. There are multiple allele systems – like the human ABO blood group where A and B are codominant to each other, but are both dominant to O. There is epistasis, where alleles at one locus are controlled by alleles at another: mice have a black fur allele dominant to a brown fur allele, but neither of them will have an effect and the mouse will be albino if a different gene has two recessive albino alleles. Then there are traits like height, weight, skin color, and many more where the appearance of the individual is determined both by a large number of genes and environmental factors.
The point of this whole rant is that genes only rarely work in a simple Mendellian dominant/recessive way. There is a whole continuum of different ways that genes can behave.
The great majority of mutations are harmful to the individual. As any life form is an incredibly complex interaction of chemicals, that is hardly surprising. Rarely, however, a mutation happens that actually makes something work better. If said mutation is significantly better suited to the environment, then – whether recessive, dominant, or other – it will soon make up a significant proportion of the population due to the increased success of the decendants of the bearer of the mutant allele.
And yes, it may take millions of years for significant changes due to evolution to occur. Specifically, if the population is large, well mixed, and not heavilly being selected for, evolution will be quite slow. For instance, pigeons, rats, dandelions, widespread tree species, things like that may not evolve much for eons. However, if populations are small, seperated, or facing strong selection pressure, evolution can happen very rapidly. For example, populations on young islands like the Galapagos or Hawaiian Islands, populations facing rapid environmental change, species split by mountain formation, rivers, canyons, etc.
OK, rant over. Y’all may continue. (In my defence, I hale from Kansas, so seldom is the chance I have to get a good evolution rant in.)