This is a pretty tricky question. I wrote an answer a long time ago for /u/parallelpain, but I have Thomas Figueira's contribution to Powell's Companion to Sparta (2018) in front of me and it's probably time I gave it another shot.

There are 2 things we must always bear in mind when we think about Spartan demography:

1. Spartiates (full Spartan citizens) were required to pay dues in kind (barley, wine and pork) to support the common messes. If they could not pay their mess dues they were stripped of their citizen status. But they were not allowed to have a profession that would allow them to buy what they needed on the market. It had to be produced for them without their own labour. Therefore the only people who could be Spartiates were the owners of large agricultural estates worked by unfree labour (helots).

2. The fact that citizenship was tied to leisured status and land ownership meant that the Spartan economy was what Figueira calls a 'politicised economy'. For the Spartiates, the economy was simply one of the things that regulated access to power. Economic decisions were made for political reasons. Economic shifts had direct consequences in political life.

It's important to get these things clear from the outset, because after this, things get complicated fast.

 

Demographically, Sparta's heyday was probably in the middle of the 6th century BC, when perhaps as many as 8,000 Spartiates coexisted with an even larger number of freeborn perioikoi, supported in their status by vast numbers of helots. At the battle of Plataia in 479 BC they put into the field an army of 5,000 Spartiates, 5,000 "picked" perioikoi hoplites, 35,000 helots and another 5000 unfree light-armed warriors who were enslaved by the perioikoi. They would never field anywhere near that many men ever again.

In our few measuring points in the ensuing decades, we see perioikoi making up an ever greater share of the hoplite phalanx, probably to make up for falling Spartiate numbers. At Sphakteria, as you note, about 120 Spartiates were captured and their possible execution brought Sparta to the negotiating table with Athens. This is not necessarily because the number was considered large; it may have been a matter of principle, and also Thucydides notes that there were very prominent men among the captives. But it fits into a trend where Spartiates are becoming increasingly precious.

The battle of Mantineia in 418 BC gives us a better (though muddled) sense of the full levy, and we find that there were probably not much more than 3,000 Spartiates left. By 394 BC the number may have fallen to about 2,500. At the battle of Leuktra, an army consisting of 2/3rds of the Spartan levy contained no more than 700 Spartiates, making up a small minority of a phalanx that was by now more than 70% perioikoi. Xenophon's numbers allow us to calculate that there would have been little more than 1,200 adult Spartiates at this time. That is the context for the death of 400 Spartiates at that battle - 1 in 3 citizens killed in a single day. A few decades later, Aristotle helpfully confirms for us that there were fewer than 1,000 Spartiates remaining.

Now, it's important to stress that we have good evidence only for the decline in the number of Spartiates. The situation for the other major groups in Spartan society is less well attested and we're not sure about hard numbers. But we have reason to assume that many of these groups (but not all) also suffered decline (but for different reasons) which had a feedback effect on the fall of Spartiate numbers. But instead of making vague gestures at context, let's go back to the start.

 

What happened to all the Spartiates and their subjects who fought the Persians at Plataia?

The main cataclysm was a major earthquake in 465 BC. As many as 45% of the Spartiate class, gathered in the urban centre of Sparta, perished when their houses collapsed. There followed, first, a helot revolt and a protracted war against the rebel stronghold in Messene; second, a critical labour shortage in Lakonia as helots joined the rebellion; and third, a phase of social mobility as some lost their citizenship status due to the loss of helot labour while others inherited several families' worth of estates that had no other surviving heirs. You can see how the fates of different groups are interrelated. Sparta was a subsistence economy propping up a parasitic leisure class; there was very little room for disruption without critical strain on the system.

Figueira suggests that the upheaval following the earthquake may have been the setting for a reform to the Spartan inheritance system that was later blamed for causing many structural problems. The reformer's intent was to free up the rule of father-to-son inheritance so that families could split up their estate and keep as many of their children as possible within the Spartiate class. It backfired spectacularly: families took the opportunity to consolidate wealth and start bidding wars of dowries to marry into prominent families. These things made inequality worse and pushed many Spartiates out of the citizen body.

Unfortunately the rest of the 5th century BC wasn't about to make things easier for Sparta. Athenian raiding during the First Peloponnesian War and the Archidamian War caused loss of life and interruption of farming. When the Athenians began to build bases, such as at Pylos, helots began to run away, causing further loss of labour. The result of both forms of disruption was that even more Spartiates could no longer afford their mess dues. And since the principle of the Spartan state was that helots served the Spartiate class only, anyone who lost his citizenship also lost what remained of his helot labour. The Spartiate "survivors" had no interest in stopping the bleeding, since those helots flowed right back into their labour pool.

All these processes did actually produce two forms of demographic surplus. First, the Spartiates who lost their citizenship didn't simply disappear into the ether. They formed a new underclass called the Hypomeiones (Inferiors), impoverished but still eligible for military service. Second, the dissolution of the helot populations serving former Spartiates may have created an actual surplus of enslaved people. This may be one of the reasons why the Spartans increasingly relied on enfranchised helots to reinforce their armies from the Peloponnesian War onward. If this is true, Inferiors and helots allowed the Spartans to keep fielding large armies despite their own dwindling numbers, and to keep on pretending there was nothing rotten in Sparta.

But by the 4th century BC, the problem with the Spartiates was coming to a head. First, it's likely that the continued disruption of the Lakonian countryside in the constant warfare of the period caused Spartiate families to adopt a cautious single-heir policy to safeguard their citizen status. After all, smaller plots were just not likely to keep someone reliably able to pay their mess dues. The result was a citizen population that ceased to replace itself.

This was worsened by the fact that Sparta in this period started to suffer serious battlefield losses. Almost every dead Spartiate now extinguished a citizen family, with their property (again) being largely absorbed by the wealthier households. Serious blows like the defeats at Lechaion (390 BC) and Tegyra (375 BC) left gashes in a citizen body that was already struggling to maintain its numbers in peacetime. Meanwhile, the helots and perioikoi they were using as alternative military manpower were bearing the brunt of the losses in overseas and naval warfare, putting the rest of Lakonia under a similar strain as the citizen body.

Not only were there no easy solutions to this problem - since creating more estates would put more households in the "barely scraping by" category, and these households were likely to collapse again at the next crisis - but Spartan society and hegemony created many incentives to make the problem worse. Competition for status and influence encouraged prominent families to accumulate more and more wealth. The path to power and wealth lay in attaining the command over a garrison or expedition abroad, so it was in the interest of the rich to keep the wars going. Their citizen armies may have shrunk further and further, and consisted to a larger and larger extent of perioikoi, but the new state treasury and their own moneyed wealth would always keep them comfortably supplied with Hypomeiones and mercenaries, and Spartan prowess would keep their subject allies in line. What could go wrong?

 

This is, more or less, the bubble that burst at Leuktra. The loss of 400 citizens (and another 600 perioikoi) could not be sustained. The victorious Thebans then marched into the Peloponnese and liberated Messene, stripping Sparta of nearly half its agricultural land and helot population, which drastically reduced the number of Spartiates there could possibly be. The century and a half that followed saw nothing but continued concentration of wealth in ever fewer hands, so that by the later 3rd century BC all the land in Lakonia was owned by just 100 Spartiate families.

The point here is that it was not the loss of just 400 men, in itself, that made Leuktra such a disaster. It was the combined loss of ever more precious citizens, of heirs to estates and enslavers of helots, of Spartan prestige, and of the integrity of Spartan territory that caused a hegemony of two centuries to collapse in a day.