NEW YORK—Investigators sought answers Monday for why safety doors failed to close when fire broke out in a New York high-rise, allowing thick smoke to rise through the tower and kill 17 people, including eight children, in the city’s deadliest blaze in more than three decades. A malfunctioning electric space heater apparently started the fire Sunday in the 19-story building in the Bronx, fire officials said. The flames damaged only a small part of the building, but smoke poured through the apartment’s open door and turned stairwells into dark, ash-choked death traps. The stairs were the only method of escape in a tower too tall for fire escapes. Fire Commissioner Daniel Nigro said the apartment’s front door and a door on the 15th floor should have been self-closing and blunted the spread of smoke, but the doors stayed fully open. It was not clear if the doors failed mechanically or …