Is it permissible to divorce one's wife if she has given birth to triplets three consecutive times? And what are the legitimate Sharia reasons that would justify such a divorce, if any?

A woman has no role in giving birth to twins, as this is in the hands of Allah the Almighty, as stated in the Noble Verse: "To Allah belongs the dominion of the heavens and the earth; He creates what He wills. He grants to whom He wills female [offspring], and He grants to whom He wills males. Or He combines them [as] males and females, and He renders whom He wills barren. Indeed, He is Knowing and Competent."

A woman who gives birth to twins is more deserving that her husband hold onto her, not divorce her, because our religion guides towards increasing offspring. The Prophet (peace be upon him) said: "Marry the affectionate and prolific, for I will boast of your numbers before the nations."