I'm not sure how much you can take away from it, but I suggest the video game L.A. Noire. The whole thing is based on getting enough evidence to arrest/convict a suspect. Its also structured with a sort of hidden countdown clock so that even if you miss a clue or botch an interrogation, something else drives the plot forward in a non-optimal way. For example, if you fail to get information from questioning, maybe the person you questioned tries to lose pursuit and get to their hiding spot. Now your objective is to follow them without being seen and they'll lead you to another area to investigate.
I guess its actually more of a reverse countdown clock. Actions happen if certain thresholds haven't been reached yet. The game grades your investigation on stars but there's no reason it can't be something else. To use your example, maybe they find out that Old Man Withers is the killer but not that he's a werewolf. They lock him up an everything's fine until the next full moon. Then Old man Withers transforms, breaks out of the cell in the jailhouse and kills the night guards.