There is no such thing as "statistically impossible," and this year is nuts. But let's get real. The polls have gotten everything right this year. Trump got the nomination after leading the Republican primary polls throughout the entire contest. Clinton beat Sanders after leading him in the polls the entire time.
And aside from that narrow window between the conventions, Clinton has led Trump all along. And Trump is sinking fast, with little time left. Here's where they stand now.
The polls could all be wrong, except for those screwy LA Times polls that have shown Trump ahead, and even they now put it at a tie. That looks less likely with each new poll, though. Trump is just losing. Badly.
I've been saying for a while that it would take a major economic collapse or a terrorist attack for Trump to win, occasionally appended with a reference to Putin trying to intervene, like with the DNC hacks. We are getting to the point, though, that we need to take an economic collapse off the table. The 2008 collapse didn't happen over night. There was a build-up that began with a recession starting in December of 2007. Unless major banks are cooking the books, like the Greek government was when it collapsed, or something like that, there just isn't enough time for a total collapse. Even a major stock market crash probably couldn't do it.
Terrorism? Let's be clear. It would have to be 9/11 scale, not some dumbass with a homemade bomb or AR15 who pledged allegiance to ISIS on facebook because his girlfriend left him. Possible? Sure, but it's been 15 years, and we have less than a month to go. Probability? Low, and not the 11% that PredictWise currently gives Trump.
On the topic, though, it is worth pointing out that normally, national security crises are associated with a "rally round the flag" effect, in which the president's approval rating goes up. See, in particular, the work of Richard Brody. However, the effect relies on "elite consensus," and, um, that wouldn't happen. The Republican Party wouldn't rally around Obama. They'd do the opposite. It is worth noting, though, that this would be a deviation from historical norms.
So what's left? More Putin hacks? It would have to be a doozy. A real scandal, like a demonstrable quid pro quo, but Clinton would never be stupid enough to admit that in an email. And even with a quid pro quo corruption thing, it would probably have to be big, given the extent of Trump's troubles. If it were as simple as agreeing to make a phone call as Sec. State to help out a Clinton Foundation donor with some minor dispute, then quid pro quo or not, it would be too minor to overshadow Trump's mess.
And that's the point here. I'm having trouble constructing plausible scenarios of Trump winning. Am I willing to rule it out? No. This year is too crazy to rule anything out. But let's be clear here. Trump winning? That would be crazy at this point. Like, major party nominee caught on tape bragging about sexual assault, crazy. Oh, wait...