Historically, states begin to "fall" once they stop expanding.
Expansion involved wars and conquests. Territories were absorbed, enemy kings were made clients, the conqueror's culture was adopted by the conquered.
However, once "peace" was attained, expansion would cease.

The state, probably an empire by then, would have become too big, and the army would simply perform guard duties at the borders.
Less soldiers would be required for that, and the citizenry, reveling in the riches of supremacy, would grow fat and lose the thirst for dominance.

At that time, enemies would emerge, seeking to destroy the giant.
And more often than not, they succeeded.
When an expanding polity seats back, after beating anyone out there to beat, it naturally begins to lose its power.
The barbarian's axe is just the final blow.

To remain in shape, you must continue working out at the gym.
To remain at the top of the industry, you must continue practicing your art.
Once you relax, your loss begins; and the fact that someone else isn't relaxing is enough reason why you'll be beaten.

There is no peacetime.
It's a constant struggle to become the best, and then remain the best.
"Can you get to the top?" is as important as "Can you remain at the top?"