For Natel: you have 2 arguments in your post. On one hand, you state, that it's is "highly unlikely" that scent would remain for months. But then say that her tracks going to and from the school would still be there. Either the scent lasts or it doesn't. Also the scent around the school is in an urban location: concrete, hard surface, lots of people and cars going through the area which that scent is in a location which people tend to think degrades faster then something in a wilderness or rural location.
I've also experimented around with my dogs (and anyone's elses that would give it a try) and we found that the wider range in trail age that you can expose the dog to, the less a factor trail age is. What I saw was that the hotter the track (ei fresher) the more wider some aspects of the trailing work was. The older, or colder, the trail was the tighter it was. Which makes me think that the skin cell fluff was gone, and the dogs were working off the lipid (fats) and/or other human chemical signature by-products which are stickier and adher to surfaces better.
Which brings up another issue of hot-track versus cold-track dogs. Not all dogs or even all dogs within a certain breed are created equal. Not all perform at equal levels. That does not make this dog or that one bad, it just means one dog may be more suited to a particular task then another which is why many trailing folks have more then one dog. I've seen some outstanding German Shepards work trails that put the Bloodhounds to shame. And vis-a-versa. Having this breed or that one does not equate to automatic success. Also how the dogs are trained make a difference.
Most LE dogs are hot-track patrol dogs. Most cue off ground scent disturbance or maybe the fear scent the suspect puts off. Department of Corrections dogs are trained to follow institutional scent more then individual scent. Most SAR trailing dogs tend to focus on only training in the timeframe they would get called out in which is 1-5 days old.
Which is why it's hard to say dogs can't do this or that. The variations are huge across the trailing dog world. I've run a dog on a 3 day old track and encountered problems but take a similar trail 7 days later and the dog slam-dunks it. Go to run what you think is a straight forward little trail and an hour later struggle to finish it in a positive fashion. You never know what the dog will do until it actually goes to do it.
For SarX: I agree that people need to experiment and try to see what works for them and how the dog responds under various conditions. I'm not ready to label anything as "impossible" as my dog has humbled me and handed me my head several times when he did something I thought was impossible. As a result I try to keep an open mind and when I hear of something weird, immediatly run home and try it with my dogs.