By "complications" I assume we're talking about conflicts or some other form of upset from the "normal" conditions the house experiences. This is relevant because the house, despite being highly characterized and personified, is still just a house, and seems to have been largely unaffected and unchanged by the world outside from the day of the nuclear war to the day the story takes place.
Most of the complications take place during the fire:
- The house shuts its doors on the fire, but the heat breaks the windows in the doors.
- The house starts to run out of water because it's used up so much of its reserve supply on daily chores, and the city utilities haven't functioned in years.
- The attic contains additional chemical-based fire retardants, which briefly halt the fire's advance.
- The fire "cleverly" burns along the outside of the house, destroying the brain that controls the attic.
- The fire begins to scramble the house's control of itself; the kitchen begins cooking breakfast, which "feeds" the fire.
- At this point the house's efforts are no longer concerted, and a few useless gestures, such as mice cleaning the ashes, hint at the hopelessness of the situation.