Based on context, and that later Rabbi Ezra mentions it in context of Ames asking if Ezra said anything to a visitor, it sounds like there is a tradition where you can ask someone for a period of time before they go to the authorities.
"Rabbi, I don't think you would anyhow; you're too much the old Loonie.
You're simply trying to chivvy me into hiring you. Mmm. I claim the Three
"Interesting. Did you send him to ask me who was
offering a reward for you and the amount of the reward?" "I certainly did
not! Did you tell him anything?" "My dear sir! You asked for the
traditional Three Days."
My text search of the book doesn't bring up any other cases where it's capitalized like that, so I don't think there really is a further explanation. It's just a plot device.