Tankless heater that only works in the morning
Shot in the dark here, but is it possible it only works when you don't have other gas appliances running (furnace, dryer, stove etc.)?  Some of the tankless units draw massive BTU's (199,000+) and you might not have enough of a supply to your house to run the tankless and another gas appliance.  I wanted to recently upgrade to a tankless but didn't because it would have required replacing my gas meter and about 50ft of blackpipe just to get enough gas capacity for everything running at once.

Also, your intake should really be using outside air.  Is the unit installed in a confined space?  Or is the space it's installed very tightly insulated/sealed from outside air penetration?