Baffled

If your CO alarm is more than 5 years old (some newer ones just coming out will go for 7), pitch it and get a new one. They don't last forever and can trip breakers. You need a detector you can trust, it's not just for looks. However it could be faulty even if it is newer than 5 years. Try a new one and if the problem persists consult an electrician.

Ignore the votedown; I have given accurate information.

Could be...but the detector seems ok. The light is still on. Though it could be faulty as you suggest. But the confusion, for me, is that the breaker isn't being tripped. With the detector plugged in, the lights and power in the room are fine. Unplug it and they go out. Plug it back in and they go on. No breaker involved. And to me that just makes no sense. I mean I can't understand how that's even possible.

Perhaps there's an intermittent connection issue is at the power receptacle. I'd check out the receptacle. No matter what the cause is there's no short involved, so the circuit breaker doesn't trip.

Yes. Exactly what I was thinking. What is happening is an interruption. maybe a connection is loose behind the outlet or it is cracked or damaged. I would check if the effect is only produced by the CO detector being in or out of the receptacle, or whether any other plug will do the same thing.

I would NOT consider getting the outlet receptacles off the wall and looking behind unless 1. I had killed the power to the whole house 2. I knew exactly what I was doing. In the absence of the latter being the case, I would get an electrician. A loose connection can generate heat and might cause damage and even lead to a fire, so I would not leave it.