I'll have to give this a try. I've noticed that sometimes I can get a lock in a matter of seconds and sometimes it takes about two or three minutes. I've had some success with doing a power cycle on the Band before starting my run, but that doesn't always seem to help.
That can depend on how fresh the almanac data is, and if any GPS satellites are hiding behind local obstructions.
What may seem to be identical conditions for you is completely different once you look at where the satellites are. I haven't seen any informaiton if the Band uses AGPS or just GPS. (AGPS uses the phone's data link to download the almanac.)
GPS satellites are constantly on the move - and they don't come back to the same position 24 hours later. So what may seem to be identical conditions (same time, same place) really are completely different conditions. Regardless of the brand or model, anyone who uses a GPS a lot has stories about "bad GPS day" where the unit just will not get a lock.
Now, that said, I think most GPS users have reported a perception that a GPS will get a lock quicker if they're not moving. It would make sense that the logic would have a better chance of working out the solution from the different possible solutions if the data isn't constantly changing.