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.