I was told once that if they don't ask for them in 12 hours, people think it's okay to wait 2 or 3 days.
If you ask the schedulers BEFORE you run the route, many of them will gladly give you 24 hours, or noon the next day, or make some accommodation. I think the short window is because a late report may be the only clue they have that a shopper is flaking so the sooner they spike it and get it back on the board again, the faster they can get it done.
I'm going through the Gold certification video and one of the things the woman said in the first segment was that 25% (!!!!) of shops that are claimed get flaked on. That is a HUGE percentage, and probably why some of us "see" the better shops and many newbies continue only seeing $5 and $10 shops for a very long time. If they don't take it seriously, they may not get to "take" much at all. Integrity is everything, and reliability is key.
But if the scheduler knows your work and knows you're not a flake, they will often give you more time after a route. The ones who won't -- do them first, and do the others after a good night's sleep.
But you can always ask.
Time to build a bigger bridge.