Glenn Fleishman, writing for Macworld on a recent change to Touch ID authentication in iOS 9:

When iOS 9 was released, Apple updated its list of cases in which iOS asks for a passcode even when Touch ID is enabled. A previously undocumented requirement asks for a passcode in a very particular set of circumstances: When the iPhone or iPad hasn’t been unlocked with its passcode in the previous six days, and Touch ID hasn’t been used to unlock it within the last eight hours. It’s a rolling timeout, so each time Touch ID unlocks a device, a new eight-hour timer starts to tick down until the passcode is required. If you wondered why you were being seemingly randomly prompted for your passcode (or more complicated password), this is likely the reason.

This explains why I’ve been seeing the passcode prompt during the weekends (when I stay up late and occasionally sleep more than 8 hours).