Due to the shortage of time, if it is not possible to perform Ghusl immediately, then it is permissible to eat Suhur while in a state of Janabah (sexual impurity).
It is narrated from Hazrat Abu Bakr bin Abdul Rahman ( رضی اللہ عنہما ) that he said : “I went with my father to (the house of) Waleed bin Hisham. We reached there and found Hazrat Aisha Siddiqa ( رضی اللہ عنہا) in service. She said:”
اَشْهَدُ عَلَی رَسُولِ اﷲِ إِنْ کَانَ لَيُصْبِحُ جُنُبًا مِنْ جِمَاعٍ غَيْرِ احْتِلَامٍ ثُمَّ يَصُومُهُ ثُمَّ دَخَلْنَا عَلَی اُمِّ سَلَمَةَ فَقَالَتْ مِثْلَ ذَلِکَ
(بخاري، الصحيح، 2: 681، رقم: 1830، بيروت، لبنان: دار ابن کثير اليمامة)
(مسلم، الصحيح، 2: 780، رقم: 1109، بيروت، لبنان: دار احياء التراث العربي)
“I bear witness that if the Prophet of Allah ﷺ experienced Janabah (sexual impurity) due to nocturnal emission (ihtilam) or intercourse and the morning arrived while he was in that state, he would observe fasting. Then, we would attend the service of Hazrat Umm Salamah ( رضی اللہ عنہا ), and she would also affirm the same.”
Therefore, due to necessity, one can eat Suhur while in a state of Janabah (sexual impurity).