It is said, that the harmful alleles get eliminated from population over a period of time, yet sickle-cell anaemia is persisting in human population. Why?

Explanation

Sickle-cell anaemia still persists in the population despite being harmful because this mutation can also be beneficial in certain conditions.
The mutant `Hb^(5)` type haemoglobin is found at high frequencies (up to 20% and above) in the tropical Africa.
It is known that heterozygotes `(Hb^(s)//Hb^(A))`, having both types of haemoglobin show resistance to malarial infection because the body targets the Plasmodium falciparum infected cell for destruction . In contrast, individuals homozygous for normal haemoglobin `(Hb^(A)//Hb^(A))` suffer high mortality rates in early childhood due to malarial infection.
Thus, the allele for sickle cells has been maintained because heterozygotes have a higher reproductive success than either of the two possible homozygotes.