To pray and to perform namaz for rain is worship. Drought is the exact time for such a prayer. Worshipping and praying is not just offered to bring the rain, otherwise just because the impurity of the intention, intending to pray only for rain would not be accepted.

Sunset is the time of the evening prayers. And eclipses of the sun and moon are the times of two particular prayers known as salat-i kusuf and salat-i khusuf. That is to say, with the veiling of the two luminous signs of the night and day, God's tremendousness is proclaimed, so Almighty God calls his servants to a sort of worship at those times. The prayers are not so that the sun and moon will be revealed (whose appearance and how long the eclipses will continue have anyway been reckoned by astronomers). In just the same way, drought is the time for the prayers for rain. And the visitation of calamities and infliction of harmful things the times of certain supplications when man realizes his impotence and through his supplication and entreaty seeks refuge at the Court of One Possessing Absolute Power. Even if the calamities are not lifted despite many supplications, it may not be said that they were not accepted. It should rather be said that the time for the supplication is not yet over... (1)

Humanity, who is in need of rain for its survival and incapable of bringing it by itself, with the conscious of knowing that the only power which would bring it is Divine Mercy, takes refuge in God. Praying for rain is sincerely done for the sake of God as it is done in the other prayers. At the end of the prayer, it is supplicated to God to rescue them from the calamity of drought.

As a matter of fact, the apparent consequence of praying for rain is its coming; but the most fundamental and beneficial consequence and pious and delightful fruit of it is: Everyone understands that, neither his father, nor his house, and job give his livelihood, but a Person who holds huge clouds serving as sponge, and earth serving as plantation fields at His disposal, supplies his wants and feeds him. Even, while a little child is used to beg his mother when hungry, he understands that immense meaning in the prayer of rain with his tiny mind that there is a Person who manages this universe as if it is a house, feeds even himself, other children, and all the other mothers. If He does not, nobody would. Therefore, he says that everyone has to invoke Him, and becomes fully faithful. (2)

If drought is the time for supplications for rain, it should be done until the end of drought. Therefore, rain is going to be the end sign of leaving the prayer. Prayer should not be left just because it did not rain, it should be perpetuated until it rains.

Sources:
(1) Bediüzzaman, Sözler Yirmiüçüncü Söz
(2) Emirdağ Lahikası 1, 14. Mektup