The Spartans were famous for their military culture. Everything in Sparta revolved around war and the military. How long after Sparta's assimilation in Alexander's Empire and its successors did the military no longer become primary in the Spartan people's minds?
Sparta actually fell from prominence before Alexander the Great. After losing to Thebes at the battle of leuctra, Sparta became a marginal power that rapidly declined in importance and military strength. By the time they fell to the Romans, Sparta was merely a rump state that housed a few hundred inhabitants
Most of the Spartan might was based on fairly large professional core of their army. At the times of Battle of Leuctra, this core became so small that they fell to much smaller and more professional army of Boetian League.
Last blow to Sparta was their fucked up diplomatic relation with Alexanders Macedonia. They were excluded from the rest of greek cities and even their new "ally", Persians couldnt supply them with enough manpower and money to do serious damage to Macedonia or to sway more cities to their cause.
They laid siege to Megalopolis in 331 BC after several minor victories against macedonian garrisons, probably after they found out that Macedonian general Memnon revolted against Alexander in the north. At that point their army consisted of their own spartan troops, allied greek troops and cavalry plus around 8000 greek mercenary veterans from Battle of Issus. That was probably 20000 soldiers and they and ultimately lost to massive relief force commanded by Antipater.
After that Sparta was considered minor greek city and ultimately after roman conquest, tourist town for curious romans.