You need better diagnosis. Who did it?? Did they use a voltmeter and did they expand their explanation?
Batteries alone if charged would keep the lights on steady. What is most likely happening is a thermal breaker is tired and shutting off, then cooling, and resetting.
Put a voltmeter across the batteries while plugged in. Turn on a bunch of lights and anything that draws 12 volts such as the heater if you can stand it for a few minutes. If the things go offline you need to be measuring across the battery. If the voltage actually goes up a bit due to lack of load the converter is working fine and as I suggested your output line is opening up. Do a search for 12 volt thermal breakers and you will find some examples.
Certified Senior Electronic Technician, Telecommunications Engineer, Telecommunications repair Service Center Owner, Original owner HR 2008