My alarm clock doesn't go off sometimes - it's "frozen" as you can see in the "Alarm in..." field vs. the analog clock above. When I open the Clock app (e.g. tapping on clock on home screen), it unfreezes. It happened twice so far - Tuesday and Thursday morning and I'm using 6.2.4 beta on Mi3.
6.2.4, mi3 no problem with mi band. It's probably something wrong with your band
Try to update mi fit to latest Chinese version. That will probably update firmware on mi band and maybe solves your problem.