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.
Source: Islam Today