How do you maintain the same frequency of alleles in a population over hundreds, or thousands of years?

Not kept constant.

The frequencies of alleles will remain unchanged generation after generation if the following conditions are met:

1. Large population. The population must be large to minimize random sampling errors.

2. Random mating. There is no mating preference. For example an AA male does not prefer an aa female.

3. No mutation. The alleles must not change.

4. No migration. Exchange of genes between the population and another population must not occur.

5. No natural selection. Natural selection must not favor any particular individual.

Hardy Weinberg