One possible reason for this is that a button is stuck setting the alarm clock on its own. Try to press on each of the buttons to make sure none of them are getting stuck before trying anything else.
If this does not fix it, remember that there is a battery on the bottom of the clock to allow for time keeping to continue in the event of a power outage. This allows the alarm to still go off without using other features. You can disconnect the battery from the alarm to fix this.
One last thing, make sure that you have pressed the correct button to turn off the alarm. If you have not, the alarm will continue to go off for the time that it has been set.
Hope this helps!