I am having this problem now but I've had my Fitbit for a few years. I've never changed or taken off the band but in the last week or so, one side of the band comes lose while doing normal chores. Usually it catches but sometimes falls to the ground. One day I was chopping some wood and every chop made it come loose but it never had before.
I looked it over and what I first thought might be a small screw, now looks like a tiny piece of dried glue. I think the metal clip in the band used to be glued in and the glue came loose. The metal clip stayed in the band but was movable so the "watch" section did not clip in securely. As long as you did not do anything strenuous then it was okay. It also looks like the rubber where the clip sets might have started to deteriorate.
As I type, I have added some super glue to try and reattach the metal clip to the band. Even if this works, I suspect for only a short time. Since the guts of the watch still work then I'll pick up a new strap the next time I see one in a store or will order on line.
In my case my fitbit is well past warranty and I do wear it during most of my waking hours so I do expect some wear on the band.
