On the simplest and most literal level, the house in "There Will Come Soft Rains" is finally destroyed by a fire caused by an accident. A wind knocked down a tree branch. It fell through a window and knocked over a bottle of cleaner. The contents fell on a stove, and a fire started.
The fire spread quickly. The house's automated systems fought the fire. They shut doors, to contain the fire and cut off its air supply...but windows were broken, and so the fire kept spreading. The system's robots sprayed it with water...but the house's reserves hadn't been refilled, and so they ran out, and the fire kept spreading. The robots sprayed chemicals inside the house, to extinguish the flames...but the fire had spread outside the house, and it kept spreading, until everything was reduced to a pile of ashes.
On a larger level, the house was destroyed by entropy. All systems break down. Disorder always spreads.