This is the 6110th most frequent Turkish word.
yitirdiğini
"Yitirdiğini" means "that which (you/he/she) lost" in English.
The term 'yitirdiğini' here is utilized to express the act of losing something, which was 'hope to succeed' in this context.
Başarılı olma umudunu yitirdiğini fark ettim.
I noticed that you lost your hope to succeed.
In this example, 'yitirdiğini' is used to ask about the location of losing something, the book specifically.
Kitabını nerede yitirdiğini hatırlıyor musun?
Do you remember where you lost your book?
In this context, 'yitirdiğini' is used to refer to the loss or waste of time, signifying realization or acceptance of this fact.