What is the falling action of "There Will Come Soft Rains" by Ray Bradbury?

The falling action is the destruction of the house from the fire. 

Falling action is the part of the plot between the climax and the resolution.  The climax is the turning point of the plot, and the resolution is the ending.  In this story, a fire starts.  That is the climax.  The destruction that follows is the falling action. The house is dead in the resolution. 

The story is set in the future.  There has been some kind of apocalyptic event, such as a nuclear bomb blast.  The people that live in the house are all dead.  The house is automated, so it goes on without them as if they were still living in it.  It takes care of every aspect of their lives.  It even lets the dog in, and cleans it up when it dies. 

The house cannot protect itself from the fire.  A tree bough crashes through the kitchen window and a bottle of cleaning solvent falls into the stove. 

The house tried to save itself. Doors sprang tightly shut, but the windows were broken by the heat and the wind blew and sucked upon the fire. 

The house gave ground as the fire in ten billion angry sparks moved with flaming ease from room to room and then up the stairs. 

The destruction of the house is the falling action.  The house definitely would like to be able to put the fire out.  However, it is fighting a losing battle against nature.  The house tries to use sprinklers, and “wall sprays let down showers of mechanical rain.”  However, it is of no use.  The house follows the people in death. 

The house is described as “dying” because it is personified.  It is so alive with all of its technology that it is almost sentient.  However, the house is still not actually alive and it cannot protect itself as nature takes the house back.