Saturday is my day off of work, so I don't have the same routine of a commute where I have 40 free minutes of no activity to recharge the Band on my way home. The last few Saturdays that it was paired with my Lumia 640 XL on the Redstone builds, I would get about 14 hours of use before the battery got below 10%, and this is without doing any type of exercise tracking.
This weekend was my first Saturday back on the 10586.x builds since getting my new phone (version 10586.545 currently). As I suspected, the battery life was much improved, and I think it is due to the phone's operating system. After taking the Band 2 off the charger Saturday morning, I waited a full 24 hours before connecting it again. After sleep tracking Saturday night and a run with GPS early Sunday morning for 30 minutes, the Band was still at 34% when I plugged it in on Sunday.
One major issue I've had with the Redstone builds was Bluetooth freezing when turning it off and back on quickly. This is listed as one of the things addressed for mobile on the 14393.51 build that has only been released for PC so far. This particular issue doesn't sound like it would be related to the causing the battery drain on the Band, but maybe it will mean that other Bluetooth fixes for mobile could be addressed soon.