I have the same exact problem. I had the same problem with the iPhone4. The alarm works, mostly. But every once in a while, and it's not linked to any kind of setting change or iOS update, the alarm fails, showing a screen that says "Alarm", say, 2 hours past the alarm time (one assumes the screen has been like that since the alarm was scheduled to go off) with no sound at all. The next day, with no settings changes whatsoever, the alarm will work perfectly normally again.
I think what everyone with this problem wants to know is what is happening at the moment the alarm goes off that is causing the alarm to fail, sometimes. Mostly it works, sometimes it fails, for unknown reasons. But it remains an ungoing bug that really does need a fix.
It's a bug. How do we fix this bug?