The one I have has some sort of issue with the connection between the ship and the base. It will stay on for a little while and then it shuts off and I need to lift it off and re-seat it :confused. I think the problem is in the connection in the ship with no way to get too it. Also my nacelles have the oil in the frosting issues.
I am a Trek fan and like the model but it has been a huge quality disappointment for the price. :angry
Get a voltmeter and measure the voltage on the plug, make sure it isn't the plug that is intermittant.
I do recall an issue with spinning the ship on the stand that could cause the internal mechanics to fail in regard to the socket.
Someone had pulled the deflector off and shown the problem.