Reading ta’awwudz prayer is Sunnah in every rak’ah, as Allah Ta’ala:
“If you read Al Qur’an ye ask refuge with Allah from Satan the accursed.” (An Nahl: 98).
And this opinion is the most authentic in the Shafi’i madhhab and reinforced by Ibn Hazm (See al Majmuu ‘III/323 and Tamaam al Minnah 172-177).
“I seek refuge in Allah from Satan the accursed, from semburannya (which menyebabkn crazy), of arrogance, and from hembusannya (which causes damage to morality).”
(Hadith narrated by Al-Imam Abu Dawud, Ibn Majah, Daraquthni, Justice and by him and by Ibn dishahkan Hibban and Dzahabi).