Certain times carry a special promise that dua is more readily answered, and the wise believer tries to catch them. The greatest is the last third of the night, when, as the Prophet taught, Allah descends to the nearest heaven and says, 'Who is calling upon Me, that I may answer him? Who is asking of Me, that I may give him?' (Sahih al-Bukhari 1145) — this is why qiyam al-layl is so treasured. The short window between the adhan and the iqamah is also singled out as a time when dua is not rejected (Sunan Abi Dawud 521). Other favoured moments include the last hour before Maghrib on Friday, while prostrating in sujood, immediately after the obligatory prayers, while fasting and at the moment of breaking the fast, during rainfall, and while traveling or facing genuine hardship — since these are all states of humility or exertion in Allah's obedience. None of this means dua is refused at other times; Allah hears every call. But deliberately seeking Him out in these blessed moments — especially the last third of the night — is a sunnah that transforms an ordinary request into a moment of real closeness to Allah.
Q&A · Dua & Dhikr
When are the best times for dua to be accepted?
References
Sahih al-Bukhari 1145Sunan Abi Dawud 521
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.