I use the alarm clock on my phone everyday and I know how important it is to have a reliable alarm clock on your phone. But don't worry because I'm here to help.
I have thoroughly researched this and did not find it to be a known issue on the LG Revere. Did this issue just recently start? Has the alarm clock worked previously on this device?
You mentioned that if you leave the reception area the alarm will not go off. Do you mean when you are in area with no service? If not please explain what you mean by reception area.
Try performing a soft reset by removing the battery for a few seconds and see if this helps. If the alarm clock still doesn't function correctly after the soft reset please post back and make sure to answer the questions above so I can further assist you.