Hmmm, this one is tough. A couple of things, some obvious but I'll mention anyway.
1. We are talking about the Alarm app that comes with the phone stock?
2. By any chance did you check your calender for an alarm reminder that is set for daily repeats?
3. What happens if you leave the alarm turned completely off? Does it still alarm at the original time?
4. When you open up your alarm application you will see three different alarm settings available. If you hit menu you can add more, did you?
5. Back to alarm application, touch the top alarm time and a settings menu should pop up. Select an alarm tone. Select Done. Go to the next alarm time and repeat however select a different alarm tone, select Done and repeat these steps for each alarm event on your phone making sure the tones are different for each one. Select one and only one of the alarms for the time you would like it to alarm each day, leave the others in the "unchecked" state. Let's see what happens and which alarm tone goes off at the "old programmed time".
As you can probably guess, the actions in #5 above are kind of a last resort to see if there is something bogus with one of the alarm settings that is not displaying or updating to the current status. By having a different alarm tone we hope to find the culprit which I would then totally Delete the setting and re-add back in using the Menu, Add alarm function. Alternatively, you can delete all settings in your alarm clock app and re-add from scratch but this will eliminate the "hunt".