I think you're mixing a few things here.
"Challenge and Response":
is an expression to go through procedures, meaning one guy asks, the other guy answers, i.e. "Landing Gear?" - "down, 3 greens!".
Your extract from the 767 refers to a checklist. Checklists are most commonly handled this way.
Technical Problems:
What you are referring your question to is something technical. If a crew experience a technical fault, they (normally the CMD) writes it up in the Tech Log. There it stays until an engineer repairs the fault, clears the entry, or - if in accordance with MEL (Minimum Equipment List) or CDL (Configuration Deviation List) - clears the entry without repairing it, meaning you are allowed to fly with that fault (with all the restriction that apply).
hth,
Dani