Seeking refuge from Satan when reciting the Quran
Is it necessary for someone to seek refuge from Satan before reading every chapter of the Qur’ân if he is reading more than one chapter in one sitting?
Sheikh `Umar al-Muqbil, professor at al-Imâm University
You do not have to seek refuge from Satan upon arriving at each new chapter in your reading. You should say it when you begin reading.
Allah says: “When thou dost read the Qur’ân, seek Allah’s protection from Satan, the rejected one.” [Sûrah al-Nahl: 98].
When you begin to read another chapter, you can start with invoking allah's name: “Bism Allah al-Rahmân al-Rahîm”.
And Allah knows best.