This is the 737th most frequent Turkish word.
kaybettiği
"Kaybettiği" means "that he/she/it lost" or "which he/she/it lost."
Here, 'kaybettiği' is used as a possessive form modifying 'cüzdanı', meaning 'the wallet he lost'.
Ali, kaybettiği cüzdanını arıyor.
Ali is looking for the wallet he lost.
In this usage, 'kaybettiği' modifies 'cesareti', meaning 'the courage he had lost', highlighting the lost attribute.
Kaybettiği cesareti, yeniden kazandı.
He regained the courage he had lost.
Here, 'kaybettiği' describes 'zamani', meaning 'the time he lost', indicating a loss in time.