Nothing... except for how rarely this occurs.
Not only does it occur rarely, but there are two other aspects to consider. First is how often the time aspect is subverted. You know how it works: you get to the Master's Altar at the very point the sacrifice is to take place because it fulfills the need for Dramatic Tension.
Well, ok.
I was mainly commenting on the idea that it wasn't present in the game at all. It is- although as you say, how much so is dependent upon the specific DM/Group... I've done both... Sometimes in the same campaign.

(IE I'll make number of days important, but won't track it down to the minutes it takes to get through the dungeon or something... As long as they get there on the right day, and don't say decide to set up camp the moment they get there, they'll make it to the sacrifice at the "nick of time...")
The second aspect is this: How often do the characters have meaningful choices about what direction to take next, whilst being aware of the time consequences of that action?
DM specific- I mean isn't this essentially like asking how often characters encounter skill challenges?
Although a time-sensitive campaign is fully possible, it does require the DM to do extra work; not only in running the campaign, but in calculating in advance how long actions should take. After all, there's no point in designing a "sacrifice the maiden after a week" adventure if it takes 10 days for the characters to even arrive at the volcano with the proper maiden... I'm sorry, have I got the roles of PCs and villains reversed again?
If you do run such a campaign (or adventures) where time-management is an important issue, please let us know!
Sure- I can think of a couple of examples off the top of my head.
1. Just a few months ago in my previous 4e campaign. (Now defunct because I moved across the country.)
In the campaign the kingdom the PCs lived in was going though somewhat of an upheaval. The crown had been stolen by the true kings younger brother. Those loyal to the true king, after having lost a civil war, had gone underground as a gorilla organization known as the "Grey Wolves."
The PCs had previously saved a member of the Grey Wolves (Lord Winterhaven) from being executed, and were traveling "north" to take him to a safe location.
Long story short, they had to leave Winterhaven in a temporarily safe location while they dealt with other matters... During this time they were separated (got themselves transported to a demiplane city in my campaign...) from Winterhaven, and had to try to find a way back. They met up with another member of the Grey Wolves who told them he had several ways to help them get back to the material plane.
Option 1 was a traveling caravan that would take them close to their intended location. It was leaving the next day. If they chose this option he would be able to travel with them, and lend support.
Option 2 was a ship leaving in 3 days. It would land them several miles north of their intended destination. If they chose this option, they wouldn't be able to travel with them- he would try to meet up with them on the other end but would only be able to wait for at most a week.
(They had some things they needed to finish up in their current location, so they chose the second option.)
2. A little more simple, I set up a room with a locked door. The lock on the door had to have a number of successful pick lock attempts before it was actually opened.
Each round a piece of the floor dropped away into a really deep pit.
So- Open the door before the floor is entirely gone.
3. In my old 3.5 campaign, at one point the characters had a limited time (it's been almost 5 years so I don't remember specifics) to be in different locations...They basically had to find a number of artifacts and get to a certain location before the Slaracians invaded... (Modified Scarred Lands campaign.)
(They ended up deciding the easiest way to do this would be to split into two groups... Since we had several PCs of "questionable" alignments they kind of split into the evil group and the good group... Everyone then made a separate character which ended up joining the group opposite the one they originally split into, and we ended up basically bouncing back and forth from week to week... The evil group actually started working against the good group at a point... But it ended up actually being too much work... Basically two high level 3.5 campaigns at once.)