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.
Reciting the Isti‘aathah (saying: A‘oothu Billaahi min Ash-Shaytaan Ar-Rajeem – I seek refuge in Allah from the accursed devil) when starting Quran recitation is a recommended act of the Sunnah. It is not required to recite it when repeating a verse or a Soorah or when moving from one verse or Soorah to another unless the reciter stops his recitation (with the intention not to continue) or interrupts it by engaging in external talk. In these two cases, he should repeat the Isti‘aathah if he wishes to resume the recitation. As-Suyooti said in Al-Itqaan, quoting Ibn Al-Jazari : “If he stops recitation or interrupts it by engaging in external talk, even if it is to return the greeting of peace, then (if he wishes to resume recitation) he should repeat it (Isti‘aathah). But if (the external talk is) related to the recitation, then he is not required to repeat it.” [End of quote]
Also, it is not required to repeat the Basmalah (saying: Bismillaah Ar-Rahmaan Ar-Raheem) when repeating a verse; this is only specific to repeating a Soorah. Shaykh Abdul-Fattaah Al-Qaadhi said in Al-Budoor Az-Zaahirah: “If he (the reciter) connected the last verse of a Soorah with its opening verse without a pause, like when he repeats the Soorah, it is incumbent on him to recite the Basmalah.” [End of quote]
It should be noted, though, that when the reciter starts his recitation at any part of a Soorah other than the beginning, he is given the choice either to recite the Basmalah or leave it, except for Soorah At-Tawbah. Ibn Al-Jazari said in An-Nashr: “It is permissible, when commencing recitation partway through any Soorah, except Soorah At-Tawbah, to recite the Basmalah or to leave it; the reciters have the choice (to recite it or not).” [End of quote]
Allah knows best.