Sparta has had a reputation of being a military power that was unmatched from training to their general attitude towards war. After the Peloponnesian War, Sparta saw to the demise of Athens temporarily before being defeated.
That being said, what signaled such a large decline in the military power of the Spartans? Was it a cultural change or simply an inability to adapt with the times?
Sparta declined because of a dramatic drop in their numbers of soldiers and they were never able to solve it.
Each Spartiate required a set amount of land to fund his mess fees - this allowed you to be a full-time soldier (as opposed to the militia that all other city-states used). In theory this is a self-perpetuating cycle where Spartiates would have sons and upon their deaths the land could be passed down and support another soldier-citizen. The problem was a lot of a Spartan's life was spent living in the barracks or on campaign, he didn't get to live at home with a wife until his 30's, all this affects his opportunities to make babies with the missus. Add to that the long and bloody nature of the Peloponsesian War and you see a serious erosion in troop numbers forcing them to rely more and more on helots and periokoi.
I've also seen the unusual freedom afforded Spartan women as another factor. They were given enough independence that some decided they didn't want to get married and have children (and the risks of childbirth). Also they could inherit land with full control over it and each acre owned was one the state couldn't assign to support a citizen-soldier.
In 480 the Spartans could mobilize 8,000 full Spartiates. By 418 this had fallen to around 3,000. By the time of Leuctra in 371 BCE there were a total of 1,100 Spartiates
Other commentators have answered your question well but in the context of military history, the Thebans at The Battle of Leuctra shattered the Spartan mythos though the use of innovative military tactics.
Hoplites relied on a force of men and the Thebans concentrated enough men on one flank to break the elite Spartan ranks. To mitigate their depleted ranks elsewhere on their line, the Thebans marched in an echelon, so they would engage in combat after the decisive encounter on the concentrated flank had already occurred.
The result was effective and it is said that Phillip of Macedon, who was a hostage of Thebes in his youth combined this tactic with cavalry and conquered Greece and his son, Alexander the Great put it into use against the Persians.