The chief priest of Eleusis (the hierophant) summoned potential initiates of the Eleusinian Mysteries to the Stoa Poikile in the Agora – always on the 19th Boedromion.
The date of the start of the Eleusinian procession was immovable, literally carved in stone, and was presumably linked to the harvest. Its celebration was compulsory, so clearly was wheat linked with food and living, and Persephone with eventual death, its opposite.
During the Persian wars Xerxes sacked Attica and the Athenians fled to the island of Salamis. On the 19th Boedromion 480 BC the Athenians were too busy preparing for what would become known as the battle of Salamis, and failed to hold the procession.
Instead, the historian Herodotus (VIII.65) records, a procession of non-humans rose up from the underworld, first to enact the procession, and then to help the Athenians defeat the Persians on the following day. The Greeks still believed their mythical heroes assisted them in times of need, and that Theseus had helped them defeat the Persians at Marathon.
Since Eleusis was tied to the fate of Greeks, their ancestors in Hades could not let it celebration lapse. Two Greeks amongst the Persian camp saw 30,000 ghosts take part in the march, in reverse, from Eleusis; if the ghosts represent the numbers that took part in the procession each year, it suggests that the entire population of Athens joined in. Although we can doubt the authenticity of the episode, it underlines the idea that Eleusinian Mysteries could not be instituted at another time of year, nor elsewhere: they were location specific, as well as time specific.
So important were the Mysteries of Eleusis, that when men were otherwise engaged, the gods intervened to ensure than the Persian non-believers did not conquer Greece and prevent them from taking place. This is not an event that occurred at any other cult or sanctuary.
Another anecdote clarifies how inflexible the date of the celebration of the Eleusinian Mysteries was.
Pythodorus is recorded as the dadouchos (torch-bearer, second priest) who had to explain to the Macedonian king Demetrius Poliorketes why he could not be initiated into the Mysteries when he wanted, during a random month of his royal choice.
The Athenians needed to appease Demetrius – this successor of Alexander was after all the king who kept his whores in the Parthenon – but they could not alter the sacred calendar.
Instead they changed the name of the month of Mounichion (April) in 302 BC: first to Anthesterion (February), so that Demetrius could be initiated into the Lesser Mysteries at Agrae, then to Boedromion (September) for the Mysteries at Eleusis.
The letter of religious law was kept.