The past 2 morning my alarm has failed to go off at all, this is since updating to gingerbread via kies, before that i had no issues with the alarm.
Ive noticed the alarm works if the clock is left as an open application, if i close all active applications the alarm fails to go off.
Sorry, no resolution, but adding that I too, have the same issue. It seems more random for me. Sometimes it works, sometimes not. For example, for the last 4 days the alrm will not work, regardless open as application, using a 3rd party alarm etc. Right now I am looking at the words (in a third party app, "Next alarm: 6:30am...and its 7:30am". It should be saying "Next alarm 1 day from now(24 hours)"
I am going to add a bombshell, It was happening a couple weeks before my Gingerbread update, which, obviously has not fixed the problem.