In 405 BC, when the Spartan admiral Lysander destroyed the Athenian fleet at Aigospotamoi. The war was over within a year.

The longer answer is more complicated. Of course, since the Peloponnesian War wasn't a single war but several wars fused together by Thucydides, there was at least one point prior to 404 BC when Athens had had enough and sued for peace. This happened after the loss of its crucial colony at Amphipolis and the disastrous attempt to regain the city in 422 BC. A peace treaty (known as the Peace of Nikias) was signed in 421 BC; it mostly arranged to cancel the conquests of both sides and return to the situation before the war broke out in 431 BC. So if you're interested in the final point at which the Athenians knew they would suffer the defeat they indeed suffered in 404 BC, you're really only asking about the Ionian or Dekeleian War of 414-404 BC.

Now, right at the start of this war, Athens suffered a major disaster: it lost the final naval battle at Syracuse and its whole expeditionary force in Sicily was wiped out. The Athenians lost more than half of their fleet, thousands of citizens, and a total force of around 40,000 men, to say nothing of the outrageous sums of money wasted on the campaign. Shortly after that, most of their island subjects revolted from the Athenian Empire, supported by a Spartan fleet. At this time a Spartan army was already permanently garrisoned in Athenian territory, effectively making it impossible for the Athenians to leave the city or make use of their farms. Really the only way to describe the Athenian position in 412 BC is "f***ing dire". But they had no thought of giving up, as Thucydides points out:

Nevertheless, with such means as they had, it was determined to resist to the last, and to provide timber and money, and to equip a fleet as they best could, to take steps to secure their allies, and above all Euboia, to reform things in the city upon a more economical footing, and to elect a board of elders to advise upon the state of affairs as occasion should arise. In short, as is the way of a democracy, in the panic of the moment they were ready to be as prudent as possible.

-- Thuc. 8.1.3-4

While the oligarchic coup of 411 BC was partly intended to get a good peace with Sparta, the resulting regime of the Four Hundred failed so spectacularly (losing the island of Euboia, where the Athenians had stored their cattle for safekeeping, as well as failing to secure the support of the Athenian fleet) that it was soon overthrown again. Athens reverted to business as usual: fight the war tooth and nail, and never let the Spartans have the satisfaction.

As it happened, though, their rump fleet still seemed to have the advantage over the one the Spartans built to challenge their rule of the sea. The Athenians won a victory at Kynossema in 411 BC and then decisively destroyed the Spartan fleet at Kyzikos the following year. In the course of the ensuing years, while the Spartans negotiated with Persia to fund the rebuilding of their naval strength, Athens actually managed to bring nearly all of its revolted allies back into the fold. Raising additional revenues from these allies, they largely managed to stabilise the situation despite the fact that their enemies were now backed by the richest power in the world. In 406 BC, when the new Spartan fleet threatened to block the grain trade through the Hellespont, the Athenians sailed out and destroyed it again at the battle of Arginousai.

At this point, according to some sources, it was actually the Spartans who sued for peace - but the Athenians refused. Puffed up by their victory, they thought they could secure even better terms if they let the war go on a little longer. So at least as late as 406 BC, even though their way to sustain their naval activity was increasingly desperate (using emergency funds, squeezing their allies for money, and rewarding enslaved people with freedom in return for naval service), they did not think they were going to lose in the end.

The fatal blow came suddenly and unexpectedly. The Athenian fleet was gathered at Aigospotamoi to keep the Hellespont clear of yet another Spartan fleet, this time led by Lysander. This cunning commander made a habit of sailing out to face the Athenian fleet, and then withdrawing without fighting a battle, day after day. Eventually the Athenians came to despise him as a coward, and no longer even bothered to sail out and match his battle line - at which point, of course, he attacked, catching most of the Ahenian ships on the beach and their crews miles away buying grain at the market of Sestos.

Xenophon gives a sense of the weight of this defeat in his account of when the news reached Athens:

It was night when the Paralos arrived at Athens with news of the disaster, and a sound of wailing ran from Peiraieus through the long walls to the city, one man passing on the news to another; and during that night no one slept, all mourning, not for the lost alone, but far more for their own selves, thinking that they would suffer such treatment as they had visited upon the Melians, colonists of the Lakedaimonians, after reducing them by siege, and upon the Histiaians and Skionaians and Toronaians and Aiginetans and many other Greek peoples.

On the following day they convened an Assembly, at which it was resolved to block up all the harbours except one, to repair the walls, to station guards, and in all other respects to get the city ready for a siege.

-- Xen. Hellenika 2.2.3-4

This, then, was the moment when Athens knew it was going to lose, and lose utterly. Lysander sailed around uprooting Athenian garrisons and settlers throughout their crumbling empire, increasing the pressure on food stores at home; there were no Athenian ships left to stop him. Then he laid siege to the city. Within months, the starving Athenians surrendered.