The first step will be to determine if the power is being lost altogether or the system is overloading and then resetting.
Try disconnecting your door from the opener and see if there is any change. If the opener lift trolley now moves then the door has too much weight or drag for the opener to handle. Test your door balance and weight. If the door moves freely and without much effort, or the trolley still does not move with the door disconnected, you might have some failure inside the opener itself that is causing binding or drag.
Another possibility could be an intermittent connection somewhere that opens due to the movement or vibration as the opener engages. Typically in a situation like that, however, the power loss and return would not happen at consistent times as you noted. If that is the case then the motor will not be hot since it is loses the power supply altogether rather than overheating due to an overload. It could be a bad connection in the power outlet, opener cord, or internal wiring or components of the opener. Try moving the cord around and see if the light on the opener flickers or goes off. You can also try an extension to another outlet to test if works better there.
There is more information in the links below that might be helpful. If the tests and information noted here do not help, you may want to consult a professional for more in-depth testing or feel free to resubmit another question with more detail on the test results and we will do our best to help further.