Do you mean you are completely turning the power off? Or is it just on standby?
If you are tunring off the phone completely, then I think the alarm does not work -- as you know ;-) Must have the phone on.
If the problem is when it is on Standby and not going off. Check the alarm volume (you will need the app Toggle Settings or Audio Manager to do this as it can;t be controlled from the standard settings menu)