The maiden example was just an example, but its a useful example. There does not need to be a clearly stated conditional time pressure on every mission. But DMs should always act in such a way as to allow their players to know that events happen in the world around them according to a logical, progressive time. I don't fixate on the minutes and hours of the world, but I do focus heavily on the days, beginning most adventures with a mention of the date and, after camping, reinforcing the fact that it is a new day. If you train your players right, they create their own pressure, because they are not sure what the ramifications of delay might be. Who knows how long they actually have until the big bad is summoned, the girl is killed, the treasure is spent, or the dragon summons help. If they go away and leave a situation uncontrolled, they can be fairly sure that things will likely have changed while they are gone as the other side continues to act. Or at least that is always the assumption on their part, even when I, the DM, am going to change up very little.
I guess it boils down to a play style where, while my game may revolve around the PCs, the world never does.