Recessive alleles can remain in a population in a heterozygous form where the dominant allele would mask the recessive. Sometimes the heterozygous form of the trait confers some protection i.e. Sickle cell anemia.To completely be eliminated from a population there must be something detrimental in the heterozygous state that would also eliminate the heterozygotes...which is very rare.I thought that this would be a nice place for you to stop and see if you understand the Hardy-Weinberg equilibrium. What's wrong with the above answer (and question)?
For those interested in my response, read on...
"It ISN'T impossible to eliminate recessive alleles from a population!
Consider a silly example, where the population consists of only 4 individuals. One population member has the only two recessive alleles in the population, but he's struck by lightening. Voila - recessive alleles eliminated! (This would constitute an extreme example of 'genetic drift'.)
A more plausible scenario would be if the recessive allele is deleterious (has negative effects). Contrary to what the first answerer said, even if the heterozygous individual displayed no ill effects, a deleterious effect in a 'homozygous recessive' individual is enough to eventually eliminate the recessive alleles from the population. (Sickle cell anaemia is in fact displaying the opposite phenomenon - the allele, so damaging in homozygous form, is kept in the population precisely because it has a BENEFICIAL effect in the heterozygous form.)
I think what you were getting at is the fact that recessive alleles are maintained in a population that is in HARDY-WEINBERG EQUILIBRIUM. To put it another way, recessive alleles aren't automatically driven to extinction simply because they are recessive. Though it is definitely possible to eliminate recessive alleles from a population, there must be a specific reason for this to occur. (If you're interested, the population must break at least one of the five criteria of the Hardy-Weinberg equilibrium. In other words, it must be evolving.)"