All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If your wife, by virtue of reliable doctors’ confirmation and advice, is facing problems by reason of continuous pregnancy, and this may harm her health, then it is lawful for her to go on for this surgery. If the condition is not so serious, then this operation will not be allowed, because Almighty Allah dispraised those who play mischief with lives. Allah Says (what means): {And when he goes away, he strives throughout the land to cause corruption therein and destroy crops and animals. And Allah does not like corruption.} [Quran 2:205]
You should be thankful to Allah and not believe that these children are enough. You do not know the coming days. Allah forbid! They may die, you may need children in your old age, or you may need the good offspring to supplicate for you.
For more benefit on family planning, please refer to 99184, 97251, 84436, 82154 and 87155.
For more benefit on permanent birth control, please refer to Fatawa 119261, 83837, 134895, 87304, 87155, 89857 and 84086.
Allah knows best.