The Mystery of the 4:00am Alarm

There's something in my house. It's an alarm. Or a watch, or toy, clock, stopwatch, or electronic device of some sort.
For approximately one week it has been going off in the vicinity of 4:00am. The vicinity of it's location, however, is completely unknown. Mr. Smith was certain it was under the couch, but a thorough search yesterday evening proved otherwise. I thought (and still think) that it's in the toy box or surrounding area, but we haven't been able to pinpoint it.
The problem is that at four o'clock in the morning we are all too asleep to track it down. It beeps for about a minute and then stops, and I go back to sleep, vowing once again that today is the day I will figure it out.
I thought I had it-- this morning I determined, in my half-asleep state, that it was the same beeping sound my kitchen timer makes. The boys assure me that there is no way to set that timer to go off at daily intervals. I concede.
There's no telling how long this could go on.