Considering it goes out completely it sounds like a problem with your AC connection to the monitor.
I recently had one like that and it was traced to a AC pin on the machine side connector that the monitor plugs into.
The pin was not seated firmly into it's housing and I could press on it with my finger and the pin would slip out the back of the connector.
I pulled it back in and felt it snap in place but the problem continued on and off so I ended up re-pinning the wire and it held, no more problem with intermediate power.