In fact, there are a few fairly logical reasons that would explain why BLM’s support has gone down that don’t really have anything to do with Biden and that wouldn’t affect his electoral prospects:
1. The surge in support for BLM came in the wake of constant media coverage of Floyd’s death, which was recorded on video and depicted hard-to-defend behavior from the police. It’s not surprising that those numbers gradually came back to earth once media coverage of Floyd and the resulting protests became less pervasive.
2. Second, BLM is a social-activist movement, not an electoral or political organization. BLM activists aren’t conducting endless polling and trying to maximize public support, and they generally keep some distance from party politics. In fact, in the weeks after Floyd’s death, Black Lives Matter activists started pushing controversial ideas, such as defunding the police, and controversial tactics, such as blocking traffic when they were protesting. I doubt it shocked BLM activists that defunding the police, in particular, was not popular. And I would assume that at least some of the dip in BLM’s popularity among white Republicans and white independents stemmed from its embrace of cutting police funding, in addition to the rioting.
3. Finally, as BLM started taking more controversial stands — particularly defunding the police — Republican politicians started attacking those positions. Voters often follow cues from the elites in their party, so it’s not surprising that BLM has grown more unpopular with Republicans and some independents.