What should we expect to happen to the frequency in the population? We should expect it to stay roughly constant, because there's no positive selection pressure.
If there is still an influx of new copies due to mutation, then the frequency will increase because there's now less selection pressure driving the mutations out.
Influx of new copies for most alleles is generally negligible for any specific allele. Examples like Huntington's are extremely rare. The probability that any mutation will arise more than once in the population is generally extremely small. Standard genetic models often don't even bother taking into account the chance that a mutation will be matched because the chance is so small.
A recent entry from the West Hunters blog (written by Gregory Cochran and Henry Harpending with whom most LWers are probably already familiar with) caught my eye:
Seems quite coherent. It meshes well with findings that the more children parents have the less they subscribe to nurture, since they finally, possibly for the first time ever, get some hands on experience with the nurture (nurture as in stuff like upbringing not nurture as in lead paint) versus. nature issue. Note that today urban, educated, highly intelligent people are less likley to have children than possibly ever, how is this likley to effect intellectual fashions?
Perhaps somewhat related to this is also the transition in the past 150 years (the time frame depending on where exactly you live) from agricultural communities, that often raised livestock to urban living. What exactly "variation" and "heredity" might mean in a intuitive way thus comes another source short with no clear replacement.