iPhone alarm clock sometimes doesn't work
I have written up a procedure for you to try:


Restore your phone.
Test - if successful go to last.
Take your iPhone to the nearest Apple store and tell them what's happening.
Test the issue with the refurbished iPhone they gave you to replace the one that was malfunctioning - if successful go to last.
Enjoy your "15 more minutes" feeling.


Failing all of these, your alarm is going off and you're sleeping through it because you stayed up too late playing WoW, drinking, coding, whatever. It eventually stops making noise and leaves the message on the screen. Try placing the phone across the room so you have to get up to turn it off. See if that helps. Either way, now you have a newly refurbished iPhone 4.

Please forgive the snarky nature of this answer. I wrote it after my alarm didn't go off in the morning due to a push notification.