شَهْرُ رَمَضَانَ الَّذِي أُنزِلَ فِيهِ الْقُرْآنُ هُدًى لِّلنَّاسِ وَبَيِّنَاتٍ مِّنَ الْهُدَىٰ وَالْفُرْقَانِ فَمَن شَهِدَ مِنكُمُ الشَّهْرَ فَلْيَصُمْهُ وَمَن كَانَ مَرِيضًا أَوْ عَلَىٰ سَفَرٍ فَعِدَّةٌ مِّنْ أَيَّامٍ أُخَرَ يُرِيدُ اللَّهُ بِكُمُ الْيُسْرَ وَلَا يُرِيدُ بِكُمُ الْعُسْرَ وَلِتُكْمِلُوا الْعِدَّةَ وَلِتُكَبِّرُوا اللَّهَ عَلَىٰ مَا هَدَاكُمْ وَلَعَلَّكُمْ تَشْكُرُونَ
2:185
The month of Ramazan is that in which the Quran was revealed, a guidance to men and clear proofs of the guidance and the distinction; therefore whoever of you is present in the month, he shall fast therein, and whoever is sick or upon a journey, then (he shall fast) a (like) number of other days; Allah desires ease for you, and He does not desire for you difficulty, and (He desires) that you should complete the number and that you should exalt the greatness of Allah for His having guided you and that you may give thanks.
The Ayah 2:185 says that whoever is present in the month one has to fast for entire month. What is problem in permitting for sex during nights ? Some people may not be comfortable if such permission is not given