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.
We have not come across any authentic hadeeth that highlights the cause of the death of Faatimah, may Allah be pleased with her.
There is a hadeeth which was reported by Imaam Ahmad in his Musnad that states that she was sick, but the scholars classified it as weak.
It is not permissible to speak about such a matter without any authentic source or hadeeth, but if it is proven that she was sick, then this was not a deficiency in her. Her father died after he became very ill and was affected by the poison which the Jewish woman put in meat and gifted it to the Prophet in the year of Khaybar.
Such an affliction is a reason for having one’s sins forgiven and one’s rank raised. ‘Abdullah ibn Mas‘ood, may Allah be pleased with him, narrated, “I visited the Prophet during his illness, and he was suffering from a high fever. I said, ‘You have a high fever. Is it because you will have a double reward for it?’ He said, ‘Yes, for no Muslim is afflicted with any harm but that Allah will make his sins fall just as the leaves of a tree fall.’” [Al-Bukhaari]
Allah knows best.