That is not always the case. Many times clients just create a new note with an nostr:nevent1qqs... reference, meaning the quoted reply note can survive whatever its replying to.

You see this in action when you see a note with a quote reply and it's content is: "This note is not available on any of your relays" 

 Yeah, I just meant that even broadcasting might lengthen the time the note will exist, as the new relays start counting from the beginning.