I'm happy to conclude that, this issue is now resolved by Airtel.
Have to suffer for 37 days, but in the end a smart technician made some frequency adjustments nearby & was 100% sure that this will fix the issue & it really did.
Been in touch with Basic Support, Nodal Team, Appellate Team, Airtel TRAI team, 121 Team & in the end, a single person who understood the problem fixed it for me.
Thank you everyone for your inputs.