When you set an alarm for your watch in the app that is not repeating on any day, it will work the first time properly. But if you later reuse that alarm and set a new time, it will look like its turned on in the app, but it won't actually ring. This is probably due to the "Repeat on" checkbox suddenly being turned on but none of the days being selected. I don't know why the "Repeat on" checkbox keeps turning on, I'm not actually pressing it, it turns on automatically whenever I change the alarm.
This is probably the worst thing an alarm can do: it looks like its turned on, but it actually isn't. Great when you rely on it to wake you up in the morning!!