The Spartan warriors are known as fierce and courageous. They’ve famously never surrendered. Even the movie 300 emphasizes that point. Spartan warriors are trained to die on the battlefield since they are young boys.
As for the premise that they’ve never surrendered, and never retreated, there is only one exception. The Spartan army has retreated from a battle only once in its history.
That battle was during the Peloponnesian war, a battle between Sparta and Athens, two of the most powerful cities during the Ancient Greece. The war saw multiple swings of momentum.
The Spartans had very simple strategy. They wanted to invade Athenian territory of Attica, destroy the farmland, and then threaten Athens itself. Athens, on the other hand, had a strategy based on their navy.
Few years into the war, the Spartan army launched an attack on Pylos, an Ahtenican-held fortress. The natural port was protected by the long island of Sphacteria. The island was located in the Peloponnesus area, one controlled by Spartans. Therefore, it was logical Sparta to want to drive the Athenians out.
The Spartan army landed their soldiers on the shore, near the fortified town, and then launched an amphibious attack. However, the Spartans could not break through the beach, and were forced to retreat. The documentary explains the entire battle.