Like you I use the phones alarm to wake up and this has happened to me on occasion, it's not a problem with the phone, or rather it's not a serious problem. Pulling the battery will fix all sorts of ills. I'm not technically proficient enough with the phone to explain what happens when the clock gets sketchy like that but it doesn't seem to cause lasting problems.
It doesn't seem to happen often so I wouldn't worry unless it does start becoming a frequent occurrence. Perhaps you should try pulling the battery every couple of weeks or so.