It is claimed that if Fatimah (s) was the rightful owner of Fadak, Imam Ali (a) must take it back during his leadership and caliphate. But, Imam Ali (a) wrote: "Fadak was only our property, while some people were jealous of it. God, the Almighty, is the best Judge of all".
Fatimah (s) protested to Abu Bakr emphasizing her rightful ownership of Fadak because she wanted to keep the justice and tradition of the Prophet (s) alive. She did not protest over any palm trees or sheaves of wheat rather she did it to prevent the Ignorance Era’s values and norms from coming back to the Islamic society. The same reason was behind Imam Ali’s forbearing to return Fadak to Fatimah’s descendants during his caliphate. He stated in the letter to Uthman Ibn Hanif explaining why he did so and gave the judgment to God. Imam Ali (a) wrote: "Fadak was only our property, while some people were jealous of it and some were not. God, the Almighty, is the best Judge of all, having or not having Fadak does not change me as we all die leaving our property behind. Ibn Abi Al-Hadid, also, in analyzing Imam's narration stated, "Imam (a) was displeased with the situation of Fadak and left it to God to judge. [1]
Also, Imam al-Sadiq (a) said that Imam Ali (a) followed the Prophet (s) as he forbore to return his house after Mecca was opened by Muslim troops as the Prophet’s cousin Aqil, Imam Ali’s brother, sold it without the Prophet’s permission. The prophet (s) responded to the person who asked that why do you not take back your house, saying “we are the family who does not take back their property if it was wrung from us.”[2]
[1] http://en.wikishia.net/view/Fadak
[2] Bihar al-Anwar, v 29, p, 395-396.