The Messenger of Allah ﷺ used to fast until we would say he did not intend to break his fast, and he would go without fasting until we would say he did not intend to fast. Every night he would recite Surah Bani Israil and Surah az-Zumar.
حدثنا حسن حدثنا حماد يعني ابن زيد عن أبي لبابة العقيلي قال
كان رسول الله ﷺ يصوم حتى نقول ما يريد أن يفطر ويفطر حتى نقول ما يريد أن يصوم وكان يقرأ في كل ليلة ببني إسرائيل والزمر
Its isnad is sahih. Abu Lubaba Aqeeli is Marwan, the freed servant of Ayesha, so it is said, and he is trustworthy. Tirmidhi graded his hadith sahih and also graded it hasan.The second part of the hadith was narrated by Tirmidhi, 5/181, no. 2920, where he said, hasan gharib, and likewise at 475, no. 345, and by Nasai in Amal al-Yawm wal-Layla, no. 712, and by Ibn Khuzayma, no. 1163. Hakim graded it sahih, 2/434, with its wording and chain, and Dhahabi passed over it in silence. As for the first part, it has already been mentioned many times.