The adapter has a red light when we turn the power on at the mains. When it's not connected to the Xbox, it will be orange until we plug it in.
Since this happens at the start, it's not an overheating problem.
After we reset the power at the main enough times, the power does work, and it does not fail as long as we don't turn off the console.
Has anyone ever had this problem and/or know if a new power supply will fix this?