I find some of the best experiences in roleplaying games to be close scrapes. You just barely beat the villain and his goons, some of you either badly injured or on the cusp of death. You just make it to the train station in time to catch your quarry as they’re about to board the departing train. You get the clue in the nick of time. Those are moments folks tend to remember and I try to provide those experiences.
However, don’t force it because the opposite experience can be just as good if the players made it happen. Maybe they stop the villain in the first round with an absolutely crushing blow. Possibly they figure out who they’re trying to pursue before that person even leaves their house and they just get them on the way out. Maybe the very first clue is enough to figure out the case. Those situations are okay too. If your players are clever, let them have that not-even-close win.