How does the recesive sickle-cell allele stay in the gene pool

Because natural selection selects for it. Thus it persists.

Explanation:

You have to understand heterozygote advantage. Basically, it's where heterozygotes have an advantage over homozygotes. In the case of sickle cell disease, heterozygotes have an advantage, and natural selection favors whatever is advantageous. Thus, because heterozygotes each have one recessive sickle-cell allele, as natural selection favors the heterozygotes, the recessive sickle-cell allele persists and remains in the gene pool.