Does the stereo have a clock and timer?

Yes it does. That was our first thought, but we checked and it's not on. Also the thing turns on a different times of the day.

Do you have cats? They can be sneaky little things!

Really though, if it isn't a timer and no remotes have a button stuck in, I'm stumped. Likely a bad microprocessor in the clock timer section.

It may be time to get the service techs on this one.