Why won't my smoke detector stop intermittently beeping?

I have a smoke detector that is actually hard wired; however, it still has a 9-volt battery for backup in case of electrical failure. Originally, it went off to indicate that the 9-volt needed to be replaced; I did so. This solved the problem, temporarily. Unfortunately, most mornings I now wake up at 6:00 because the alarm starts with a loud beep every 30 seconds or so. This thing is driving me crazy! Any help would be greatly appreciated.