My Band's battery life was cut down to a day after the anniversary update. I suspected that the Band and my Lumia 950 were communicating more frequently, but it didn't seem to have a meaningful impact on notifications. It was the Health app update last Thursday that seems to finally fix Bluetooth functionality, but the excessive battery drain seemed to persist.
I now have the Band paired with my iPhone 7 and battery life is back up to 2 days. Notifications also work more reliably than they ever did on the 950. Except, of course, for the aforementioned update on the last day I was using that phone.