So first of all, it's not genes which are dominant or recessive, it's alleles. Alleles are variants of genes. For example, there's a blood type gene with alleles A, B, and O. You generally have two alleles of each gene, since you have two copies of (most) genes.

Alleles are dominant or recessive as a side effect of how they work. For example, consider a gene that's involved in melanin production. It's got an allele that makes melanin normally. And it's got an allele with a mutation that makes it not work. A cell will activate this gene if it senses the cell doesn't have enough melanin.

If you have two copies of the working allele, you get melanin. If you have one copy of the working allele and one of the busted allele, you get melanin. If you have two copies of the busted allele, you get no melanin. So the working allele is dominant.

Now, to get back to your question, can this change? Well...no. Because if an allele changes, it becomes a different allele. An allele is a specific version of a gene. If you mutate it in some way, you make a new version of that gene, a different allele.

Dominance and recessiveness aren't even absolute things, they depend on which other allele you are comparing to. For example, go back to A B O blood types. A is dominant over O, but it's not dominant over B. If you have A and O alleles, you just have type A blood. If you have A and B alleles, you have AB type blood. So is A dominant, or not?