How to make my alarm as stable as a server?
I also use Desire and this has never/ever happened to me under any circumstances. Alarm would not work if you had killed it but you have clearly specified you don't have any task killer.

As you said there is Snooze/Dismiss screen, the alarm indeed went on. Are you sure you didn't miss when the alarm rang at the correct time? Or are you sure the volume is loud enough?