Why do we still have genetic disorders that show anticipation?
I can think of 3 explanations (not mutually exclusive) for the maintenance of important genetic disorders that prevent the sick carrier to reproduce.


Following what you said, the frequency of a given allele in a population is influenced by selection, drift, migration and mutation. Some disease present at low frequency can typically spontaneously de novo appear in a population. This is typically the case of cancer and trisomy 21 where new mutations (mutation in the broad sense) likely explain a big part of why such disease do not disappear through time. 
Many genetic disease are carried out by recessive alleles. In consequence, only homozygotes for the recessive allele express the disease and the disease can persist through drift. Note the interesting case of hemophilia and Malaria resistant where the heterozygote actually has higher fitness than any homozygote (heterozygote advantage), particularly in regions where there is a high prevalence of malaria. In this case, the disease is not washed out of the population not only due to drift but also due positive selection on the heterozygotes.
Many so-called genetic disease actually have an important environmental component. For the Huntington's disease, the carrier of the autosomal dominant mutation does not necessarily express the disease. From wikipedia:



  The disease is caused by an autosomal dominant mutation in either of an individual's two copies of a gene called Huntingtin, which means any child of an affected person typically has a 50% chance of inheriting the disease.


As a result the Huntington's disease can still segregate thanks to drift in the healthy heterozygotes.