I had never heard the "untying the bracelet and throwing it" theory until your post. I thought, like _alicesprings, that Brian was just fiddling with it and then swung his arms. I just rewatched those last frames three times and can't tell. I can see that Brian is fiddling with it for quite a long time, though since it is shown in slow-motion, that might not actually be true. Using NFL replay rules, if there isn't clear and definite evidence, the ruling on the field stands, so I have to go with my initial assessment that Brian didn't untie and then throw away his bracelet.
I am not sure why Brian stopped wearing it. One theory I've read, but discounted, is that it was Gale's own bracelet and when fans started copying him, he stopped wearing it.