Even brand-new, best brand tire chains fall off if you turn the wheels while beginning to move. Like, say, when you're moving away from a mail box you just filled.
The (barely) good news was that the new chains are easier to put back on. While it does require lying full length in the icy snow while you grab the other end, that's about the worst of it. Even though I was only doing a third of the route (the parts I hadn't finished on Saturday) I still landed up putting the chains back on five different times. Sigh.