Hector's last fight

A prime example is Hector trying to flee Achilles during their final duel in Book 22 of the Iliad. Hector was a celebrated warrior, the greatest of the Trojans and commander of their army. By the time of his ill-fated duel with the best of the Achaeans, he had survived an earlier duel with Achilles (mentioned briefly in Book 9), one with Protesilaus (whom he killed), and one with the second greatest of the Achaeans, Telamonian Ajax (a tie).

Here's how Homer describes the moment the mighty Trojan prince realizes he stands no chance against the enraged Achilles:

So he pondered as he abode, and nigh to him came Achilles, the peer of Enyalius, warrior of the waving helm, brandishing over his right shoulder the Pelian ash, his terrible spear; and all round about the bronze flashed like the gleam of blazing fire or of the sun as he riseth. But trembling gat hold of Hector when he was ware of him, neither dared he any more abide where he was, but left the gates behind him, and fled in fear; and the son of Peleus rushed after him, trusting in his fleetness of foot. Homer. The Iliad. Translated by Murray, A T. Loeb Classical Library Volumes. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1924.

The two run around the walls of Troy three times until Hector regains his courage and decides to fight.

Interestingly, Paris, Hector's younger brother, also fled a duel (Book 3), with a little bit of help from Aphrodite. This time it was against Menelaus and their duel was an attempt to end the war. It should be noted, however, that Paris is described by Homer as lacking in military prowess - especially in comparison to his brother. He probably doesn't quite fit your definition of a powerful figure of martial might.

Typhon & the flight of the gods to Egypt

In another example from Greek mythology, when the serpentine storm giant Typhon attacked Olympus, the gods - except Zeus, Athena and in some versions Dionysus - disguised themselves as animals and fled to Egypt in panic.

Here's a version of the story, as told by Antoninus Liberalis:

Typhon was the son of Ge (Gaea, Earth), a deity monstrous because of his strength, and of outlandish appearance. There grew out of him numerous heads and hands and wings, while from his thighs came huge coils of snakes. He emitted all kinds of roars and nothing could resist his might. He felt an urge to usurp the rule of Zeus and not one of the gods could withstand him as he attacked. In panic they fled to Aigyptos (Egypt), all except Athena and Zeus, who alone were left. Typhon hunted after them, on their track. When they fled they had changed themselves in anticipation into animal forms. Apollon became a hawk [i.e. the Egyptian god Horus], Hermes an ibis [the Egyptian god Thoth], Ares became a fish, the lepidotus [Egyptian Lepidotus or Onuris], Artemis a cat [Neith or Bastet], Dionysos took the shape of a goat [Osiris or Arsaphes], Herakles a fawn, Hephaistos (Hephaestus) an ox [Ptah], and Leto a shrew mouse [Wadjet]. The rest of the gods each took on what transformations they could. When Zeus struck Typhon with a thunderbolt, Typhon, aflame hid himself and quenched the blaze in the sea. Zeus did not desist but piled the highest mountain, Aitna (Etna), on Typon and set Hephaistos on the peak as a guard. Having set up his anvils, he works his red hot blooms on Typhon's neck. Antoninus Liberalis, Metamorphoses 28 (trans. Celoria)

If you wish to find out more, Theoi Project, an invaluable online reference, has extensive information on Typhon. Wikipedia's Typhon article is also quite comprehensive.