The month of Shabaan is also called as “Shahrus Salaah”
The verse of Durood was revealed in the month of Shabaan and the command for Durood was given to us in this month, so for this reason we are asked to send a lot of Durood on the Holy Prophet Mohammed (ﷺ) in this month. As given in Ghuniya Lit talibi tariqil haqqi, Vol. 1, Pg No: 188:
Translation: In this month the doors of good/mercy are opened and blessings descend, sins are forgiven and wiped out and lots and lots of Durood is sent to the presence of the Holy Prophet Mohammed (ﷺ), who is the best of all creation and this month is the special month to send Durood and Salam on the Holy Prophet Mohammed (ﷺ)
Hazrath Shaykh Ul Islam A’arif Billah Imam Muhammad Anwarullah Farooqui (May Allah sanctify his soul), the founder of Jamia Nizamia writes on the authority of “Fuyuzaate Rabbaniya sharh Adhkar Nawaviya:”
Hazrath Shaykh Muhammad bin Ali relates on the authority of Hafidh Abu Dharr Haravi that the commandment for Durood was revealed in 2 Hijri and some (scholars) say that it was in the month of Sha’abaan, that’s why the month of Sha’abaan is called “Shahrus Salaah” (the month of Durood and Salam)
(Anwar-e-Ahmadi Pg No: 61)
Ref : www.ziaislamic.com