I too am currently running BBS. Not the challenge though, only for bench, squat, and deadlift. I am running BBB for the press.
I just finished the 2nd week of the 2nd cycle. My plan is to deload after the 3rd cycle. However if I remember correctly in Forever when talking about the 7th Week Protocol: Deload I think you CAN deload after ANY 5/3/1 cycle if you feel you need it. However if you are deloading after every cycle that may not be doing the “challenge” though.
So far I have felt I haven’t needed the deload and don’t think I will. But I have had a few “bumps and bruises along the way” especially after squat day. I had a old injury flare up a bit, but I focused on sleep and eating enough and its improved enough that I am not worried. Personally I discovered I need to cut out all lower back assistance when squatting and deadlifting this much volume.
The big thing is making sure your TM is at a solid 85% or lower. If you start with the correct TM, eat enough, and get your sleep right you shouldn’t need to deload until after the 3rd cycle of BBS, before you move into your Anchor.