In English there is a proverb; “Third time’s the Charm.” It implies that on the third attempt one will meet with success. Apparently, Homer didn’t know that proverb because in the Iliad it is more like “Three times and Then.” Most famously;
(Patroclus) “was making a terrifying shout, and he killed three times nine men. But when he [= Patroclus] rushed ahead for yet a fourth time, equal [īsos] to a superhuman force [daimōn], then, O Patroclus, the end of your life made its appearance to you.” (Iliad 16.785-787) Center for Hellenic Studies trans.
Rather than being slain like Patroclus, Diomedes is warned off by Apollo on his own fourth attempt at the god Apollo. (Iliad 5: 432-442) It only takes Poseidon three strides and with the fourth he reaches his goal—Aigai (Iliad 13:20)
Thrice did swift-footed radiant Achilles spring towards him spear in hand, and three times did he waste his blow upon the air. When he rushed forward for the fourth time as though he were a superhuman force [daimōn] he shouted aloud saying, “Hound, this time too you have escaped death— (Iliad 20:445-450)
Asteropaios vainly tried to draw Achilles’ spear out of the bank by main force; three times and amid the fourth attempt Achilles slew him. (Iliad 21:175) Again famously, the sad scene in Book 22 where Achilles chases Hector around the city,
"Then, at last, as they were nearing the fountains for the fourth time, the father of all balanced his golden scales and placed a doom in each of them,  one for Achilles and the other for Hector, breaker of horses. As he held the scales by the middle, the doom of Hector fell down deep into the house of Hādēs”
Three times Zeus thundered from the heights of Ida as a sign and then Hector saw Zeus was minded to grant victory. [Iliad 8:175] Thrice Odysseus cries out as loudly as man can cry, and three times did brave Menelaus hear him. Only then Menelaus turns and says “Ajax, noble son of Telamon, chief of your people, the cry of patient Odysseus rings in my ears.” [Book 11:465] Three times Hector tries to drag Patroclus’ body away by the feet (18:155) and would have succeeded the fourth, but the goddess Iris summoned Achilles. (18:165) “Thrice did radiant Achilles raise his loud cry as he stood by the trench, and three times were the Trojans and their brave allies thrown into confusion [18:230]” and then the Achaeans with great joy recover Patroclus’ body. At the funeral games Ajax and Diomedes spring at one another three times with murderous intent and then the crowd parts them.
“Thrice did he drag it round the tomb [sēma] of the son of Menoetius, and then went back into his tent, leaving the body on the ground full length and with its face downwards. But Apollo would not suffer it to be disfigured, for he pitied the man, dead though he now was; (Iliad 24:20)”
So, three time and then… is a regular motif in the Iliad. Why? I don’t know.