If you do anything other than click Okay, you will lose the BOD. The same happens on EA. Some examples include misclicking, hitting cancel, or accidentally right-clicking on the menu and closing it. This is to prevent people from "cycling" through bods to get the one that they want.
Otherwise, I tested it a few times this morning, and as long as I correctly accepted each bod I was given all three. I will leave this open though incase someone else can narrow it down more.